readme.f90

数值计算和数值分析在Fortran下的特殊函数库,是数值计算的必备

second kinds and their derivatives with arbitrary real orders and real arguments.

CIKVA   Evaluate a sequence of modified Bessel functions of the first and second
kinds and their derivatives with arbitrary real orders and complex arguments.

CIKVB   Evaluate a sequence of modified Bessel functions of the first and second
kinds and their derivatives with arbitrary real orders and complex arguments.

CIKLV   Evaluate modified Bessel functions of the first and second kinds and
their derivatives with a large arbitrary real order and complex arguments.

CH12N   Evaluate a sequence of Hankel functions of the first and second kinds
and their derivatives with integer orders and complex arguments.

*****

ITJYA   Evaluate the integral of Bessel functions J0(t) and Y0(t) 
from 0 to x using series and asymptotic expansions.

ITJYB   Evaluate the integral of Bessel functions J0(t) and Y0(t) 
from 0 to x using polynomial approximations.

ITTJYA  Evaluate the integral of [1-J0(t)]/t from 0 to x and Y0(t)/t   
from x to infinity using series and asymptotic expansions.

ITTJYB  Evaluate the integral of [1-J0(t)]/t from 0 to x and Y0(t)/t   
from x to infinity using polynomial approximations.

ITIKA   Evaluate the integral of modified Bessel functions I0(t) and   
K0(t) from 0 to x using series and asymptotic expansions.

ITIKB   Evaluate the integral of modified Bessel functions I0(t) and   
K0(t) from 0 to x using polynomial approximations.

ITTIKA  Evaluate the integral of [1-I0(t)]/t from 0 to x and K0(t) 
from x to infinity using series and asymptotic expansions.

ITTIKB  Evaluate the integral of [1-I0(t)]/t from 0 to x and K0(t) 
from x to infinity using polynomial approximations.

****

SPHJ    Evaluate a sequence of spherical Bessel functions of the 
first kind and their derivatives with integer orders and  real arguments.

SPHY    Evaluate a sequence of spherical Bessel functions of the 
second kind and their derivatives with integer orders and  real arguments.

CSPHJY  Evaluate a sequence of spherical Bessel functions of the first and
second kinds and their derivatives with integer orders and complex arguments.

RCTJ    Evaluate a sequence of Riccati-Bessel functions and their 
derivatives of the first kind.

RCTY    Evaluate a sequence of Riccati-Bessel functions and their 
derivatives of the second kind.

SPHI    Evaluate a sequence of modified spherical Bessel functions 
of the first kind and their derivatives with integer orders and real arguments.

SPHK    Evaluate a sequence of modified spherical Bessel functions 
of the second kind and their derivatives with integer orders and real arguments.

CSPHIK  Evaluate a sequence of modified spherical Bessel functions of the first
and second kinds and their derivatives with integer orders and complex arguments.

*****


KLVNA   Evaluate the Kelvin functions and their derivatives using 
series and asymptotic expansions.

KLVNB   Evaluate the Kelvin functions and their derivatives using 
polynomial approximations.

KLVNZO  Evaluate the zeros of the Kelvin functions and their  derivatives.

***** 

AIRYA   Evaluate the Airy functions and their derivatives by means 
of Bessel functions.

AIRYB   Evaluate the Airy functions and their derivatives using the 
series and asymptotic expansions.

ITAIRY  Evaluate the integral of the Airy functions. 

AIRYZO  Evaluate the zeros of Airy functions and their derivatives.

***** 

STVH0   Evaluate the zeroth-order Struve function.

STVH1   Evaluate the first-order Struve function.

STVHV   Evaluate the Struve functions with an arbitrary order.

ITSH0   Evaluate the integral of Struve function H0(t) from 0 to x.

ITTH0   Evaluate the integral of H0(t)/t from x to infinity.

STVL0   Evaluate the zeroth-order modified Struve function.

STVL1   Evaluate the first-order modified Struve function.

STVLV   Evaluate the modified Struve function with an arbitrary order.

ITSL0   Evaluate the integral of modified Struve function L0(t) from 0 to x.

*****

HYGFX   Evaluate the hypergeometric function with real arguments.

HYGFZ   Evaluate the hypergeometric function with complex arguments.

*****

CHGM    Evaluate the confluent hypergeometric function M(a,b,x) with 
real arguments.

CCHG    Evaluate the confluent hypergeometric function M(a,b,z) with 
complex arguments.

CHGU    Evaluate the confluent hypergeometric function U(a,b,x) with 
real arguments.

*****

PBDV    Evaluate a sequence of parabolic cylinder functions Dv(x) and 
their derivatives.

PBVV    Evaluate a sequence of parabolic cylinder functions Vv(x) and 
their derivatives.

PBWA    Evaluate parabolic cylinder functions W(a,+/-x) and their derivatives.

CPBDN   Evaluate a sequence of parabolic cylinder functions Dn(z) and 
their derivatives for complex arguments.

***** 

CVA1    Evaluate a sequence of characteristic values for the Mathieu 
and modified Mathieu functions.

CVA2    Evaluate a specific characteristic value for the Mathieu 
and modified Mathieu functions.

FCOEF   Evaluate the expansion coefficients for the Mathieu and
modified Mathieu functions.

MTU0    Evaluate the Mathieu functions and their derivatives.

MTU12   Evaluate the modified Mathieu functions of the first and 
second kinds and their derivatives.

*****        

SEGV    Evaluate a sequence of characteristic values for spheroidal 
wave functions.

SDMN    Evaluate the expansion coefficients d_k^mn for spheroidal 
wave functions.

SCKA    Evaluate the expansion coefficients c_2k^mn for spheroidal 
wave functions (method 1).

SCKB    Evaluate the expansion coefficients c_2k^mn for spheroidal 
wave functions (method 2).

ASWFA   Evaluate the angular spheroidal wave functions of the first 
kind (method 1).

ASWFB   Evaluate the angular spheroidal wave functions of the first 
kind (method 2).

RSWFP   Evaluate the radial prolate spheroidal wave functions of the 
first and second kinds.

RSWFO   Evaluate the radial oblate spheroidal wave functions of the 
first and second kinds.

LPMNS   Evaluate a sequence of the associated Legendre functions of the first
kind and their derivatives with real arguments for a given order.

LQMNS   Evaluate a sequence of the associated Legendre functions of the second
kind and their derivatives with real arguments for a given order.

*****

ERROR   Evaluate the error function.

CERROR  Evaluate the error function with a complex argument.

*****

FCS     Evaluate the Fresnel Integrals.

FFK     Evaluate the modified Fresnel integrals.

CERZO   Evaluate the complex zeros of the error function.

FCSZO   Evaluate the complex zeros of the Fresnel Integrals.

***** 

CISIA   Evaluate the cosine and sine integrals using their series 
and asymptotic expansions.

CISIB   Evaluate the cosine and sine integrals using their rational 
approximations.

***** 

COMELP  Evaluate the complete elliptic integrals of the first and second kinds.

ELIT    Evaluate the incomplete elliptic integrals of the first and second kinds.

ELIT3   Evaluate the complete and incomplete elliptic integrals of 
the third kind.

JELP    Evaluate the Jacobian elliptic functions.

*****

E1XA    Evaluate the exponential integral E1(x) using its polynomial 
approximations.

E1XB    Evaluate the exponential integral E1(x) using its series and
continued fraction expressions.

E1Z     Evaluate the exponential integral E1(z) for complex arguments.

ENXA    Evaluate a sequence of exponential integrals En(x) (method 1).

ENXB    Evaluate a sequence of exponential integrals En(x) (method 2).

EIX     Evaluate the exponential integral Ei(x).