SF_SPECIAL

Description

SciFortran module for specific functions and distributions

Quick access

Routines:

step(), sgn(), heaviside(), fermi(), wfun(), zerf(), bethe_lattice(), dens_bethe(), gfbethe(), gfbether(), bethe_guess_g0(), dens_hyperc(), dens_2dsquare(), dens_3dcubic(), airya(), airyb(), airyzo(), ajyik(), aswfa(), aswfb(), bernoa(), bernob(), betaf(), bjndd(), cbk(), cchg(), cerf(), cerror(), cerzo(), cfc(), cfs(), cgama(), ch12n(), chgm(), chgu(), chgubi(), chguit(), chgul(), chgus(), cik01(), ciklv(), cikna(), ciknb(), cikva(), cikvb(), cisia(), cisib(), cjk(), cjy01(), cjylv(), cjyna(), cjynb(), cjyva(), cjyvb(), clpmn(), clpn(), clqmn(), clqn(), comelp(), cpbdn(), cpdla(), cpdsa(), cpsi(), csphik(), csphjy(), cv0(), cva1(), cva2(), cvf(), cvql(), cvqm(), cy01(), cyzo(), dvla(), dvsa(), e1xa(), e1xb(), e1z(), eix(), elit(), elit3(), envj(), enxa(), enxb(), werror(), eulera(), eulerb(), fcoef(), fcs(), fcszo(), ffk(), gaih(), gam0(), gammaf(), gmn(), herzo(), hygfx(), hygfz(), ik01a(), ik01b(), ikna(), iknb(), ikv(), incob(), incog(), itairy(), itika(), itikb(), itjya(), itjyb(), itsh0(), itsl0(), itth0(), ittika(), ittikb(), ittjya(), ittjyb(), jdzo(), jelp(), jy01a(), jy01b(), jyna(), jynb(), jyndd(), jyv(), jyzo(), klvna(), klvnb(), klvnzo(), kmn(), lagzo(), lamn(), lamv(), legzo(), lgama(), lpmn(), lpmns(), lpmv(), lpn(), lpni(), lqmn(), lqmns(), lqna(), lqnb(), msta1(), msta2(), mtu0(), mtu12(), othpl(), pbdv(), pbvv(), pbwa(), psi(), qstar(), rctj(), rcty(), refine(), rmn1(), rmn2l(), rmn2so(), rmn2sp(), rswfo(), rswfp(), scka(), sckb(), sdmn(), segv(), sphi(), sphj(), sphk(), sphy(), stvh0(), stvh1(), stvhv(), stvl0(), stvl1(), stvlv(), vvla(), vvsa()

Used modules

• sf_integrate: SciFortran module for function integration

  • quad()

Subroutines and functions

interface  sf_special/step(x, i, j[, origin])

Parameters:

• x [real, in]

• i [integer, in]

• j [integer, in]

Options:

origin [logical, in]

interface  sf_special/sgn(x)

Parameters:

x [integer, real, in]

function  sf_special/heaviside(x)

Parameters:

x [real, in]

Return:

heaviside [real]

function  sf_special/fermi(x, beta[, limit])

Parameters:

• x [real, in]

• beta [real, in]

Options:

limit [real, in]

Return:

fermi [real]

function  sf_special/wfun(z)

Parameters:

z [complex]

Return:

wfun [complex]

function  sf_special/zerf(z)

Parameters:

z [complex, in]

Return:

zerf [complex]

subroutine  sf_special/bethe_lattice(dos, ome, lk[, d])

Parameters:

• dos (lk) [real]

• ome (lk) [real]

Options:

• lk [integer]

• d [real]

function  sf_special/dens_bethe(x[, d])

Parameters:

x [real, in]

Options:

d [real, in]

Return:

dens_bethe [real]

function  sf_special/gfbethe(w, zeta, d)

Parameters:

• w [real, in]

• zeta [complex, in]

• d [real, in]

Return:

gfbethe [complex]

function  sf_special/gfbether(w, zeta, d)

Parameters:

• w [real]

• zeta [complex]

• d [real]

Return:

gfbether [complex]

subroutine  sf_special/bethe_guess_g0(g0, d, beta, hloc)

Parameters:

• g0 (•) [complex]

• d [real]

• beta [real]

• hloc [real]

function  sf_special/dens_hyperc(x[, t1])

Parameters:

x [real, in]

Options:

t1 [real, in]

Return:

dens_hyperc [real]

function  sf_special/dens_2dsquare(x[, ts])

Parameters:

x [real, in]

Options:

ts [real, in]

Return:

dos [real]

function  sf_special/dens_3dcubic(x[, ts])

Parameters:

x [real, in]

Options:

ts [real]

Return:

dos [real]

subroutine  sf_special/airya(x, ai, bi, ad, bd)

Parameters:

• x [real]

• ai [real]

• bi [real]

• ad [real]

• bd [real]

subroutine  sf_special/airyb(x, ai, bi, ad, bd)

Parameters:

• x [real]

• ai [real]

• bi [real]

• ad [real]

• bd [real]

subroutine  sf_special/airyzo(nt, kf, xa, xb, xc, xd)

Options:

nt [integer]

Parameters:

• kf [integer]

• xa (nt) [real]

• xb (nt) [real]

• xc (nt) [real]

• xd (nt) [real]

subroutine  sf_special/ajyik(x, vj1, vj2, vy1, vy2, vi1, vi2, vk1, vk2)

Parameters:

• x [real]

• vj1 [real]

• vj2 [real]

• vy1 [real]

• vy2 [real]

• vi1 [real]

• vi2 [real]

• vk1 [real]

• vk2 [real]

subroutine  sf_special/aswfa(m, n, c, x, kd, cv, s1f, s1d)

Parameters:

• m [integer]

• n [integer]

• c [real]

• x [real]

• kd [integer]

• cv [real]

• s1f [real]

• s1d [real]

subroutine  sf_special/aswfb(m, n, c, x, kd, cv, s1f, s1d)

Parameters:

• m [integer]

• n [integer]

• c [real]

• x [real]

• kd [integer]

• cv [real]

• s1f [real]

• s1d [real]

subroutine  sf_special/bernoa(n, bn)

Options:

n [integer, optional/default=-1 + shape(bn, 0)]

Parameters:

bn (1 + n) [real]

subroutine  sf_special/bernob(n, bn)

Options:

n [integer, optional/default=-1 + shape(bn, 0)]

Parameters:

bn (1 + n) [real]

subroutine  sf_special/betaf(p, q, bt)

Parameters:

• p [real]

• q [real]

• bt [real]

subroutine  sf_special/bjndd(n, x, bj, dj, fj)

Options:

n [integer, optional/default=-1 + shape(bj, 0)]

Parameters:

• x [real]

• bj (1 + n) [real]

• dj (1 + n) [real]

• fj (1 + n) [real]

subroutine  sf_special/cbk(m, n, c, cv, qt, ck, bk)

Parameters:

• m [integer]

• n [integer]

• c [real]

• cv [real]

• qt [real]

• ck (200) [real]

• bk (200) [real]

subroutine  sf_special/cchg(a, b, z, chg)

Parameters:

• a [real]

• b [real]

• z [complex]

• chg [complex]

subroutine  sf_special/cerf(z, cer, cder)

Parameters:

• z [complex]

• cer [complex]

• cder [complex]

subroutine  sf_special/cerror(z, cer)

Parameters:

• z [complex]

• cer [complex]

subroutine  sf_special/cerzo(nt, zo)

Options:

nt [integer]

Parameters:

zo (nt) [complex]

subroutine  sf_special/cfc(z, zf, zd)

Parameters:

• z [complex]

• zf [complex]

• zd [complex]

subroutine  sf_special/cfs(z, zf, zd)

Parameters:

• z [complex]

• zf [complex]

• zd [complex]

subroutine  sf_special/cgama(x, y, kf, gr, gi)

Parameters:

• x [real]

• y [real]

• kf [integer]

• gr [real]

• gi [real]

subroutine  sf_special/ch12n(n, z, nm, chf1, chd1, chf2, chd2)

Options:

n [integer, optional/default=-1 + shape(chf1, 0)]

Parameters:

• z [complex]

• nm [integer]

• chf1 (1 + n) [complex]

• chd1 (1 + n) [complex]

• chf2 (1 + n) [complex]

• chd2 (1 + n) [complex]

subroutine  sf_special/chgm(a, b, x, hg)

Parameters:

• a [real]

• b [real]

• x [real]

• hg [real]

subroutine  sf_special/chgu(a, b, x, hu, md)

Parameters:

• a [real]

• b [real]

• x [real]

• hu [real]

• md [integer]

subroutine  sf_special/chgubi(a, b, x, hu, id)

Parameters:

• a [real]

• b [real]

• x [real]

• hu [real]

• id [integer]

subroutine  sf_special/chguit(a, b, x, hu, id)

Parameters:

• a [double_precision]

• b [double_precision]

• x [double_precision]

• hu [double_precision]

• id [integer]

subroutine  sf_special/chgul(a, b, x, hu, id)

Parameters:

• a [real]

• b [real]

• x [real]

• hu [real]

• id [integer]

subroutine  sf_special/chgus(a, b, x, hu, id)

Parameters:

• a [real]

• b [real]

• x [real]

• hu [real]

• id [integer]

subroutine  sf_special/cik01(z, cbi0, cdi0, cbi1, cdi1, cbk0, cdk0, cbk1, cdk1)

Parameters:

• z [complex]

• cbi0 [complex]

• cdi0 [complex]

• cbi1 [complex]

• cdi1 [complex]

• cbk0 [complex]

• cdk0 [complex]

• cbk1 [complex]

• cdk1 [complex]

subroutine  sf_special/ciklv(v, z, cbiv, cdiv, cbkv, cdkv)

Parameters:

• v [real]

• z [complex]

• cbiv [complex]

• cdiv [complex]

• cbkv [complex]

• cdkv [complex]

subroutine  sf_special/cikna(n, z, nm, cbi, cdi, cbk, cdk)

Options:

n [integer, optional/default=-1 + shape(cbi, 0)]

Parameters:

• z [complex]

• nm [integer]

• cbi (1 + n) [complex]

• cdi (1 + n) [complex]

• cbk (1 + n) [complex]

• cdk (1 + n) [complex]

subroutine  sf_special/ciknb(n, z, nm, cbi, cdi, cbk, cdk)

Options:

n [integer, optional/default=-1 + shape(cbi, 0)]

Parameters:

• z [complex]

• nm [integer]

• cbi (1 + n) [complex]

• cdi (1 + n) [complex]

• cbk (1 + n) [complex]

• cdk (1 + n) [complex]

subroutine  sf_special/cikva(v, z, vm, cbi, cdi, cbk, cdk)

Parameters:

• v [real]

• z [complex]

• vm [real]

• cbi (·) [complex]

• cdi (·) [complex]

• cbk (·) [complex]

• cdk (·) [complex]

subroutine  sf_special/cikvb(v, z, vm, cbi, cdi, cbk, cdk)

Parameters:

• v [real]

• z [complex]

• vm [real]

• cbi (·) [complex]

• cdi (·) [complex]

• cbk (·) [complex]

• cdk (·) [complex]

subroutine  sf_special/cisia(x, ci, si)

Parameters:

• x [real]

• ci [real]

• si [real]

subroutine  sf_special/cisib(x, ci, si)

Parameters:

• x [real]

• ci [real]

• si [real]

subroutine  sf_special/cjk(km, a)

Parameters:

• km [integer]

• a (·) [real]

subroutine  sf_special/cjy01(z, cbj0, cdj0, cbj1, cdj1, cby0, cdy0, cby1, cdy1)

Parameters:

• z [complex]

• cbj0 [complex]

• cdj0 [complex]

• cbj1 [complex]

• cdj1 [complex]

• cby0 [complex]

• cdy0 [complex]

• cby1 [complex]

• cdy1 [complex]

subroutine  sf_special/cjylv(v, z, cbjv, cdjv, cbyv, cdyv)

Parameters:

• v [real]

• z [complex]

• cbjv [complex]

• cdjv [complex]

• cbyv [complex]

• cdyv [complex]

subroutine  sf_special/cjyna(n, z, nm, cbj, cdj, cby, cdy)

Options:

n [integer, optional/default=-1 + shape(cbj, 0)]

Parameters:

• z [complex]

• nm [integer]

• cbj (1 + n) [complex]

• cdj (1 + n) [complex]

• cby (1 + n) [complex]

• cdy (1 + n) [complex]

subroutine  sf_special/cjynb(n, z, nm, cbj, cdj, cby, cdy)

Options:

n [integer, optional/default=-1 + shape(cbj, 0)]

Parameters:

• z [complex]

• nm [integer]

• cbj (1 + n) [complex]

• cdj (1 + n) [complex]

• cby (1 + n) [complex]

• cdy (1 + n) [complex]

subroutine  sf_special/cjyva(v, z, vm, cbj, cdj, cby, cdy)

Parameters:

• v [real]

• z [complex]

• vm [real]

• cbj (·) [complex]

• cdj (·) [complex]

• cby (·) [complex]

• cdy (·) [complex]

subroutine  sf_special/cjyvb(v, z, vm, cbj, cdj, cby, cdy)

Parameters:

• v [real]

• z [complex]

• vm [real]

• cbj (·) [complex]

• cdj (·) [complex]

• cby (·) [complex]

• cdy (·) [complex]

subroutine  sf_special/clpmn(mm, m, n, x, y, cpm, cpd)

Options:

• mm [integer, optional/default=-1 + shape(cpm, 0)]

• n [integer, optional/default=-1 + shape(cpm, 1)]

Parameters:

• m [integer]

• x [real]

• y [real]

• cpm (1 + mm, 1 + n) [complex]

• cpd (1 + mm, 1 + n) [complex]

subroutine  sf_special/clpn(n, x, y, cpn, cpd)

Options:

n [integer, optional/default=-1 + shape(cpn, 0)]

Parameters:

• x [real]

• y [real]

• cpn (1 + n) [complex]

• cpd (1 + n) [complex]

subroutine  sf_special/clqmn(mm, m, n, x, y, cqm, cqd)

Options:

• mm [integer, optional/default=-1 + shape(cqm, 0)]

• n [integer, optional/default=-1 + shape(cqm, 1)]

Parameters:

• m [integer]

• x [real]

• y [real]

• cqm (1 + mm, 1 + n) [complex]

• cqd (1 + mm, 1 + n) [complex]

subroutine  sf_special/clqn(n, x, y, cqn, cqd)

Options:

n [integer, optional/default=-1 + shape(cqn, 0)]

Parameters:

• x [real]

• y [real]

• cqn (1 + n) [complex]

• cqd (1 + n) [complex]

subroutine  sf_special/comelp(hk, ck, ce)

Parameters:

• hk [real]

• ck [real]

• ce [real]

subroutine  sf_special/cpbdn(n, z, cpb, cpd)

Options:

n [integer, optional/default=-1 + shape(cpb, 0)]

Parameters:

• z [complex]

• cpb (1 + n) [complex]

• cpd (1 + n) [complex]

subroutine  sf_special/cpdla(n, z, cdn)

Parameters:

• n [integer]

• z [complex]

• cdn [complex]

subroutine  sf_special/cpdsa(n, z, cdn)

Parameters:

• n [integer]

• z [complex]

• cdn [complex]

subroutine  sf_special/cpsi(x, y, psr, psi)

Parameters:

• x [real]

• y [real]

• psr [real]

• psi [real]

subroutine  sf_special/csphik(n, z, nm, csi, cdi, csk, cdk)

Options:

n [integer, optional/default=-1 + shape(csi, 0)]

Parameters:

• z [complex]

• nm [integer]

• csi (1 + n) [complex]

• cdi (1 + n) [complex]

• csk (1 + n) [complex]

• cdk (1 + n) [complex]

subroutine  sf_special/csphjy(n, z, nm, csj, cdj, csy, cdy)

Options:

n [integer, optional/default=-1 + shape(csj, 0)]

Parameters:

• z [complex]

• nm [integer]

• csj (1 + n) [complex]

• cdj (1 + n) [complex]

• csy (1 + n) [complex]

• cdy (1 + n) [complex]

subroutine  sf_special/cv0(kd, m, q, a0)

Parameters:

• kd [integer]

• m [integer]

• q [real]

• a0 [real]

subroutine  sf_special/cva1(kd, m, q, cv)

Parameters:

• kd [integer]

• m [integer]

• q [real]

• cv (200) [real]

subroutine  sf_special/cva2(kd, m, q, a)

Parameters:

• kd [integer]

• m [integer]

• q [real]

• a [real]

subroutine  sf_special/cvf(kd, m, q, a, mj, f)

Parameters:

• kd [integer]

• m [integer]

• q [real]

• a [real]

• mj [integer]

• f [real]

subroutine  sf_special/cvql(kd, m, q, a0)

Parameters:

• kd [integer]

• m [integer]

• q [real]

• a0 [real]

subroutine  sf_special/cvqm(m, q, a0)

Parameters:

• m [integer]

• q [real]

• a0 [real]

subroutine  sf_special/cy01(kf, z, zf, zd)

Parameters:

• kf [integer]

• z [complex]

• zf [complex]

• zd [complex]

subroutine  sf_special/cyzo(nt, kf, kc, zo, zv)

Options:

nt [integer]

Parameters:

• kf [integer]

• kc [integer]

• zo (nt) [complex]

• zv (nt) [complex]

subroutine  sf_special/dvla(va, x, pd)

Parameters:

• va [real]

• x [real]

• pd [real]

subroutine  sf_special/dvsa(va, x, pd)

Parameters:

• va [real]

• x [real]

• pd [real]

subroutine  sf_special/e1xa(x, e1)

Parameters:

• x [real]

• e1 [real]

subroutine  sf_special/e1xb(x, e1)

Parameters:

• x [real]

• e1 [real]

subroutine  sf_special/e1z(z, ce1)

Parameters:

• z [complex]

• ce1 [complex]

subroutine  sf_special/eix(x, ei)

Parameters:

• x [real]

• ei [real]

subroutine  sf_special/elit(hk, phi, fe, ee)

Parameters:

• hk [real]

• phi [real]

• fe [real]

• ee [real]

subroutine  sf_special/elit3(phi, hk, c, el3)

Parameters:

• phi [real]

• hk [real]

• c [real]

• el3 [real]

function  sf_special/envj(n, x)

Parameters:

• n [integer]

• x [real]

Return:

envj [real]

subroutine  sf_special/enxa(n, x, en)

Options:

n [integer, optional/default=-1 + shape(en, 0)]

Parameters:

• x [real]

• en (1 + n) [real]

subroutine  sf_special/enxb(n, x, en)

Options:

n [integer, optional/default=-1 + shape(en, 0)]

Parameters:

• x [real]

• en (1 + n) [real]

subroutine  sf_special/werror(x, err)

Parameters:

• x [real]

• err [real]

subroutine  sf_special/eulera(n, en)

Options:

n [integer, optional/default=-1 + shape(en, 0)]

Parameters:

en (1 + n) [real]

subroutine  sf_special/eulerb(n, en)

Options:

n [integer, optional/default=-1 + shape(en, 0)]

Parameters:

en (1 + n) [real]

subroutine  sf_special/fcoef(kd, m, q, a, fc)

Parameters:

• kd [integer]

• m [integer]

• q [real]

• a [real]

• fc (251) [real]

subroutine  sf_special/fcs(x, c, s)

Parameters:

• x [real]

• c [real]

• s [real]

subroutine  sf_special/fcszo(kf, nt, zo)

Parameters:

• kf [integer]

• zo (nt) [complex]

Options:

nt [integer]

subroutine  sf_special/ffk(ks, x, fr, fi, fm, fa, gr, gi, gm, ga)

Parameters:

• ks [integer]

• x [real]

• fr [real]

• fi [real]

• fm [real]

• fa [real]

• gr [real]

• gi [real]

• gm [real]

• ga [real]

subroutine  sf_special/gaih(x, ga)

Parameters:

• x [real]

• ga [real]

subroutine  sf_special/gam0(x, ga)

Parameters:

• x [real]

• ga [real]

subroutine  sf_special/gammaf(x, ga)

Parameters:

• x [real]

• ga [real]

subroutine  sf_special/gmn(m, n, c, x, bk, gf, gd)

Parameters:

• m [integer]

• n [integer]

• c [real]

• x [real]

• bk (200) [real]

• gf [real]

• gd [real]

subroutine  sf_special/herzo(n, x, w)

Options:

n [integer]

Parameters:

• x (n) [real]

• w (n) [real]

subroutine  sf_special/hygfx(a, b, c, x, hf)

Parameters:

• a [real]

• b [real]

• c [real]

• x [real]

• hf [real]

subroutine  sf_special/hygfz(a, b, c, z, zhf)

Parameters:

• a [real]

• b [real]

• c [real]

• z [complex]

• zhf [complex]

subroutine  sf_special/ik01a(x, bi0, di0, bi1, di1, bk0, dk0, bk1, dk1)

Parameters:

• x [real]

• bi0 [real]

• di0 [real]

• bi1 [real]

• di1 [real]

• bk0 [real]

• dk0 [real]

• bk1 [real]

• dk1 [real]

subroutine  sf_special/ik01b(x, bi0, di0, bi1, di1, bk0, dk0, bk1, dk1)

Parameters:

• x [real]

• bi0 [real]

• di0 [real]

• bi1 [real]

• di1 [real]

• bk0 [real]

• dk0 [real]

• bk1 [real]

• dk1 [real]

subroutine  sf_special/ikna(n, x, nm, bi, di, bk, dk)

Options:

n [integer, optional/default=-1 + shape(bi, 0)]

Parameters:

• x [real]

• nm [integer]

• bi (1 + n) [real]

• di (1 + n) [real]

• bk (1 + n) [real]

• dk (1 + n) [real]

subroutine  sf_special/iknb(n, x, nm, bi, di, bk, dk)

Options:

n [integer, optional/default=-1 + shape(bi, 0)]

Parameters:

• x [real]

• nm [integer]

• bi (1 + n) [real]

• di (1 + n) [real]

• bk (1 + n) [real]

• dk (1 + n) [real]

subroutine  sf_special/ikv(v, x, vm, bi, di, bk, dk)

Parameters:

• v [real]

• x [real]

• vm [real]

• bi (·) [real]

• di (·) [real]

• bk (·) [real]

• dk (·) [real]

subroutine  sf_special/incob(a, b, x, bix)

Parameters:

• a [real]

• b [real]

• x [real]

• bix [real]

subroutine  sf_special/incog(a, x, gin, gim, gip)

Parameters:

• a [real]

• x [real]

• gin [real]

• gim [real]

• gip [real]

subroutine  sf_special/itairy(x, apt, bpt, ant, bnt)

Parameters:

• x [real]

• apt [real]

• bpt [real]

• ant [real]

• bnt [real]

subroutine  sf_special/itika(x, ti, tk)

Parameters:

• x [real]

• ti [real]

• tk [real]

subroutine  sf_special/itikb(x, ti, tk)

Parameters:

• x [real]

• ti [real]

• tk [real]

subroutine  sf_special/itjya(x, tj, ty)

Parameters:

• x [real]

• tj [real]

• ty [real]

subroutine  sf_special/itjyb(x, tj, ty)

Parameters:

• x [real]

• tj [real]

• ty [real]

subroutine  sf_special/itsh0(x, th0)

Parameters:

• x [real]

• th0 [real]

subroutine  sf_special/itsl0(x, tl0)

Parameters:

• x [real]

• tl0 [real]

subroutine  sf_special/itth0(x, tth)

Parameters:

• x [real]

• tth [real]

subroutine  sf_special/ittika(x, tti, ttk)

Parameters:

• x [real]

• tti [real]

• ttk [real]

subroutine  sf_special/ittikb(x, tti, ttk)

Parameters:

• x [real]

• tti [real]

• ttk [real]

subroutine  sf_special/ittjya(x, ttj, tty)

Parameters:

• x [real]

• ttj [real]

• tty [real]

subroutine  sf_special/ittjyb(x, ttj, tty)

Parameters:

• x [real]

• ttj [real]

• tty [real]

subroutine  sf_special/jdzo(nt, n, m, p, zo)

Parameters:

• nt [integer]

• n (1400) [integer]

• m (1400) [integer]

• p (1400) [character(len=4)]

• zo (1400) [real]

subroutine  sf_special/jelp(u, hk, esn, ecn, edn, eph)

Parameters:

• u [real]

• hk [real]

• esn [real]

• ecn [real]

• edn [real]

• eph [real]

subroutine  sf_special/jy01a(x, bj0, dj0, bj1, dj1, by0, dy0, by1, dy1)

Parameters:

• x [real]

• bj0 [real]

• dj0 [real]

• bj1 [real]

• dj1 [real]

• by0 [real]

• dy0 [real]

• by1 [real]

• dy1 [real]

subroutine  sf_special/jy01b(x, bj0, dj0, bj1, dj1, by0, dy0, by1, dy1)

Parameters:

• x [real]

• bj0 [real]

• dj0 [real]

• bj1 [real]

• dj1 [real]

• by0 [real]

• dy0 [real]

• by1 [real]

• dy1 [real]

subroutine  sf_special/jyna(n, x, nm, bj, dj, by, dy)

Options:

n [integer, optional/default=-1 + shape(bj, 0)]

Parameters:

• x [real]

• nm [integer]

• bj (1 + n) [real]

• dj (1 + n) [real]

• by (1 + n) [real]

• dy (1 + n) [real]

subroutine  sf_special/jynb(n, x, nm, bj, dj, by, dy)

Options:

n [integer, optional/default=-1 + shape(bj, 0)]

Parameters:

• x [real]

• nm [integer]

• bj (1 + n) [real]

• dj (1 + n) [real]

• by (1 + n) [real]

• dy (1 + n) [real]

subroutine  sf_special/jyndd(n, x, bjn, djn, fjn, byn, dyn, fyn)

Parameters:

• n [integer]

• x [real]

• bjn [real]

• djn [real]

• fjn [real]

• byn [real]

• dyn [real]

• fyn [real]

subroutine  sf_special/jyv(v, x, vm, bj, dj, by, dy)

Parameters:

• v [real]

• x [real]

• vm [real]

• bj (·) [real]

• dj (·) [real]

• by (·) [real]

• dy (·) [real]

subroutine  sf_special/jyzo(n, nt, rj0, rj1, ry0, ry1)

Parameters:

• n [integer]

• rj0 (nt) [real]

• rj1 (nt) [real]

• ry0 (nt) [real]

• ry1 (nt) [real]

Options:

nt [integer]

subroutine  sf_special/klvna(x, ber, bei, ger, gei, der, dei, her, hei)

Parameters:

• x [real]

• ber [real]

• bei [real]

• ger [real]

• gei [real]

• der [real]

• dei [real]

• her [real]

• hei [real]

subroutine  sf_special/klvnb(x, ber, bei, ger, gei, der, dei, her, hei)

Parameters:

• x [real]

• ber [real]

• bei [real]

• ger [real]

• gei [real]

• der [real]

• dei [real]

• her [real]

• hei [real]

subroutine  sf_special/klvnzo(nt, kd, zo)

Options:

nt [integer]

Parameters:

• kd [integer]

• zo (nt) [real]

subroutine  sf_special/kmn(m, n, c, cv, kd, df, dn, ck1, ck2)

Parameters:

• m [integer]

• n [integer]

• c [real]

• cv [real]

• kd [integer]

• df (200) [real]

• dn (200) [real]

• ck1 [real]

• ck2 [real]

subroutine  sf_special/lagzo(n, x, w)

Options:

n [integer]

Parameters:

• x (n) [real]

• w (n) [real]

subroutine  sf_special/lamn(n, x, nm, bl, dl)

Options:

n [integer, optional/default=-1 + shape(bl, 0)]

Parameters:

• x [real]

• nm [integer]

• bl (1 + n) [real]

• dl (1 + n) [real]

subroutine  sf_special/lamv(v, x, vm, vl, dl)

Parameters:

• v [real, in,required]

• x [real]

• vm [real]

• vl (1 + int(v)) [real]

• dl (1 + int(v)) [real]

subroutine  sf_special/legzo(n, x, w)

Options:

n [integer]

Parameters:

• x (n) [real]

• w (n) [real]

subroutine  sf_special/lgama(kf, x, gl)

Parameters:

• kf [integer]

• x [real]

• gl [real]

subroutine  sf_special/lpmn(mm, m, n, x, pm, pd)

Options:

• mm [integer, optional/default=-1 + shape(pm, 0)]

• n [integer, optional/default=-1 + shape(pm, 1)]

Parameters:

• m [integer]

• x [real]

• pm (1 + mm, 1 + n) [real]

• pd (1 + mm, 1 + n) [real]

subroutine  sf_special/lpmns(m, n, x, pm, pd)

Parameters:

• m [integer]

• x [real]

• pm (1 + n) [real]

• pd (1 + n) [real]

Options:

n [integer, optional/default=-1 + shape(pm, 0)]

subroutine  sf_special/lpmv(v, m, x, pmv)

Parameters:

• v [real]

• m [integer]

• x [real]

• pmv [real]

subroutine  sf_special/lpn(n, x, pn, pd)

Options:

n [integer, optional/default=-1 + shape(pn, 0)]

Parameters:

• x [real]

• pn (1 + n) [real]

• pd (1 + n) [real]

subroutine  sf_special/lpni(n, x, pn, pd, pl)

Options:

n [integer, optional/default=-1 + shape(pn, 0)]

Parameters:

• x [real]

• pn (1 + n) [real]

• pd (1 + n) [real]

• pl (1 + n) [real]

subroutine  sf_special/lqmn(mm, m, n, x, qm, qd)

Options:

• mm [integer, optional/default=-1 + shape(qm, 0)]

• n [integer, optional/default=-1 + shape(qm, 1)]

Parameters:

• m [integer]

• x [real]

• qm (1 + mm, 1 + n) [real]

• qd (1 + mm, 1 + n) [real]

subroutine  sf_special/lqmns(m, n, x, qm, qd)

Parameters:

• m [integer]

• x [real]

• qm (1 + n) [real]

• qd (1 + n) [real]

Options:

n [integer, optional/default=-1 + shape(qm, 0)]

subroutine  sf_special/lqna(n, x, qn, qd)

Options:

n [integer, optional/default=-1 + shape(qn, 0)]

Parameters:

• x [real]

• qn (1 + n) [real]

• qd (1 + n) [real]

subroutine  sf_special/lqnb(n, x, qn, qd)

Options:

n [integer, optional/default=-1 + shape(qn, 0)]

Parameters:

• x [real]

• qn (1 + n) [real]

• qd (1 + n) [real]

function  sf_special/msta1(x, mp)

Parameters:

• x [real]

• mp [integer]

Return:

msta1 [integer]

function  sf_special/msta2(x, n, mp)

Parameters:

• x [real]

• n [integer]

• mp [integer]

Return:

msta2 [integer]

subroutine  sf_special/mtu0(kf, m, q, x, csf, csd)

Parameters:

• kf [integer]

• m [integer]

• q [real]

• x [real]

• csf [real]

• csd [real]

subroutine  sf_special/mtu12(kf, kc, m, q, x, f1r, d1r, f2r, d2r)

Parameters:

• kf [integer]

• kc [integer]

• m [integer]

• q [real]

• x [real]

• f1r [real]

• d1r [real]

• f2r [real]

• d2r [real]

subroutine  sf_special/othpl(kf, n, x, pl, dpl)

Parameters:

• kf [integer]

• x [real]

• pl (1 + n) [real]

• dpl (1 + n) [real]

Options:

n [integer, optional/default=-1 + shape(pl, 0)]

subroutine  sf_special/pbdv(v, x, dv, dp, pdf, pdd)

Parameters:

• v [real]

• x [real]

• dv (·) [real]

• dp (·) [real]

• pdf [real]

• pdd [real]

subroutine  sf_special/pbvv(v, x, vv, vp, pvf, pvd)

Parameters:

• v [real]

• x [real]

• vv (·) [real]

• vp (·) [real]

• pvf [real]

• pvd [real]

subroutine  sf_special/pbwa(a, x, w1f, w1d, w2f, w2d)

Parameters:

• a [real]

• x [real]

• w1f [real]

• w1d [real]

• w2f [real]

• w2d [real]

subroutine  sf_special/psi(x, ps)

Parameters:

• x [real]

• ps [real]

subroutine  sf_special/qstar(m, n, c, ck, ck1, qs, qt)

Parameters:

• m [integer]

• n [integer]

• c [real]

• ck (200) [real]

• ck1 [real]

• qs [real]

• qt [real]

subroutine  sf_special/rctj(n, x, nm, rj, dj)

Options:

n [integer, optional/default=-1 + shape(rj, 0)]

Parameters:

• x [real]

• nm [integer]

• rj (1 + n) [real]

• dj (1 + n) [real]

subroutine  sf_special/rcty(n, x, nm, ry, dy)

Options:

n [integer, optional/default=-1 + shape(ry, 0)]

Parameters:

• x [real]

• nm [integer]

• ry (1 + n) [real]

• dy (1 + n) [real]

subroutine  sf_special/refine(kd, m, q, a, iflag)

Parameters:

• kd [integer]

• m [integer]

• q [real]

• a [real]

• iflag [integer]

subroutine  sf_special/rmn1(m, n, c, x, df, kd, r1f, r1d)

Parameters:

• m [integer]

• n [integer]

• c [real]

• x [real]

• df (200) [real]

• kd [integer]

• r1f [real]

• r1d [real]

subroutine  sf_special/rmn2l(m, n, c, x, df, kd, r2f, r2d, id)

Parameters:

• m [integer]

• n [integer]

• c [real]

• x [real]

• df (200) [real]

• kd [integer]

• r2f [real]

• r2d [real]

• id [integer]

subroutine  sf_special/rmn2so(m, n, c, x, cv, df, kd, r2f, r2d)

Parameters:

• m [integer]

• n [integer]

• c [real]

• x [real]

• cv [real]

• df (200) [real]

• kd [integer]

• r2f [real]

• r2d [real]

subroutine  sf_special/rmn2sp(m, n, c, x, cv, df, kd, r2f, r2d)

Parameters:

• m [integer]

• n [integer]

• c [real]

• x [real]

• cv [real]

• df (200) [real]

• kd [integer]

• r2f [real]

• r2d [real]

subroutine  sf_special/rswfo(m, n, c, x, cv, kf, r1f, r1d, r2f, r2d)

Parameters:

• m [integer]

• n [integer]

• c [real]

• x [real]

• cv [real]

• kf [integer]

• r1f [real]

• r1d [real]

• r2f [real]

• r2d [real]

subroutine  sf_special/rswfp(m, n, c, x, cv, kf, r1f, r1d, r2f, r2d)

Parameters:

• m [integer]

• n [integer]

• c [real]

• x [real]

• cv [real]

• kf [integer]

• r1f [real]

• r1d [real]

• r2f [real]

• r2d [real]

subroutine  sf_special/scka(m, n, c, cv, kd, ck)

Parameters:

• m [integer]

• n [integer]

• c [real]

• cv [real]

• kd [integer]

• ck (200) [real]

subroutine  sf_special/sckb(m, n, c, df, ck)

Parameters:

• m [integer]

• n [integer]

• c [real]

• df (200) [real]

• ck (200) [real]

subroutine  sf_special/sdmn(m, n, c, cv, kd, df)

Parameters:

• m [integer]

• n [integer]

• c [real]

• cv [real]

• kd [integer]

• df (200) [real]

subroutine  sf_special/segv(m, n, c, kd, cv, eg)

Parameters:

• m [integer]

• n [integer]

• c [real]

• kd [integer]

• cv [real]

• eg (200) [real]

subroutine  sf_special/sphi(n, x, nm, si, di)

Options:

n [integer, optional/default=-1 + shape(si, 0)]

Parameters:

• x [real]

• nm [integer]

• si (1 + n) [real]

• di (1 + n) [real]

subroutine  sf_special/sphj(n, x, nm, sj, dj)

Options:

n [integer, optional/default=-1 + shape(sj, 0)]

Parameters:

• x [real]

• nm [integer]

• sj (1 + n) [real]

• dj (1 + n) [real]

subroutine  sf_special/sphk(n, x, nm, sk, dk)

Options:

n [integer, optional/default=-1 + shape(sk, 0)]

Parameters:

• x [real]

• nm [integer]

• sk (1 + n) [real]

• dk (1 + n) [real]

subroutine  sf_special/sphy(n, x, nm, sy, dy)

Options:

n [integer, optional/default=-1 + shape(sy, 0)]

Parameters:

• x [real]

• nm [integer]

• sy (1 + n) [real]

• dy (1 + n) [real]

subroutine  sf_special/stvh0(x, sh0)

Parameters:

• x [real]

• sh0 [real]

subroutine  sf_special/stvh1(x, sh1)

Parameters:

• x [real]

• sh1 [real]

subroutine  sf_special/stvhv(v, x, hv)

Parameters:

• v [real]

• x [real]

• hv [real]

subroutine  sf_special/stvl0(x, sl0)

Parameters:

• x [real]

• sl0 [real]

subroutine  sf_special/stvl1(x, sl1)

Parameters:

• x [real]

• sl1 [real]

subroutine  sf_special/stvlv(v, x, slv)

Parameters:

• v [real]

• x [real]

• slv [real]

subroutine  sf_special/vvla(va, x, pv)

Parameters:

• va [real]

• x [real]

• pv [real]

subroutine  sf_special/vvsa(va, x, pv)

Parameters:

• va [real]

• x [real]

• pv [real]