SF_SPECIAL

Quick access

Routines:

dens_2dsquare(), dens_3dcubic(), dens_hyperc(), fermi(), heaviside(), sgn(), step(), wfun()

Used modules

  • sf_integrate

    • sf_integrate/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]