function fundoc(varargin)
%***BEGIN PROLOGUE FUNDOC
%***PURPOSE Documentation for FNLIB, a collection of routines for
% evaluating elementary and special functions.
%***LIBRARY SLATEC
%***CATEGORY C, Z
%***TYPE ALL (FUNDOC-A)
%***KEYWORDS DOCUMENTATION, ELEMENTARY FUNCTIONS, SPECIAL FUNCTIONS
%***AUTHOR Kahaner, D. K., (NBS)
%***DESCRIPTION
%
% The SLATEC Library -- Elementary And Special Functions
%
% This describes the elementary and special function routines available
% in the SLATEC library. Most of the these routines were written by
% Wayne Fullerton while at LANL. Some were written by Don Amos of SNLA.
% There are approximately 63 single precision, 63 doubleprecision and
% 25 complex user callable elementary and special function routines.
%
% The table below gives a breakdown of routines according to their
% function. Unless otherwise indicated all routines are function
% subprograms.
% Sngl. Dble.
% Description Notation Prec. Prec. Complex
%
% ***Intrinsic Functions and Fundamental Functions***
% Unpack floating point Call R9UPAK(X,Y,N) D9UPAK --
% number
% Pack floating point R9PAK(Y,N) D9PAK --
% number
% Initialize orthogonal INITS(OS,NOS,ETA) INITDS --
% polynomial series
% Evaluate Chebyshev summation for CSEVL(X,CS,N) DCSEVL --
% series i = 1 to n of
% cs(i)*(2*x)**(i-1)
%
% ***Elementary Functions***
% Argument = theta in z = \ z \ * -- -- CARG(Z)
% radians e**(i * theta)
% Cube root CBRT(X) DCBRT CCBRT
% Relative error exponen- ((e**x) -1) / x EXPREL(X) DEXPRL CEXPRL
% tial from first order
% Common logarithm log to the base 10 -- -- CLOG10(Z)
% of z
% Relative error logarithm ln(1 + x) ALNREL(X) DLNREL CLNREL
% Relative error logarithm (ln(1 + x) - x R9LN2R(X) D9LN2R C9LN2R
% from second order + x**2/2) / x**3
% ***Trigonometric and Hyperbolic Functions***
% Tangent tan z -- -- CTAN(Z)
% Cotangent cot x COT(X) DCOT CCOT
% Sine x in degrees sin((2*pi*x)/360) SINDG(X) DSINDG --
% Cosine x in degrees cos((2*pi*x)/360) COSDG(X) DCOSDG --
% Arc sine arcsin (z) -- -- CASIN(Z)
% Arc cosine arccos (z) -- -- CACOS(Z)
% Arc tangent arctan (z) -- -- CATAN(Z)
% Quadrant correct arctan (z1/z2) -- -- CATAN2(Z1,
% arc tangent Z2)
% Hyperbolic sine sinh z -- -- CSINH(Z)
% Hyperbolic cosine cosh z -- -- CCOSH(Z)
% Hyperbolic tangent tanh z -- -- CTANH(Z)
% Arc hyperbolic sine arcsinh (x) ASINH(X) DASINH CASINH
% Arc hyperbolic cosine arccosh (x) ACOSH(X) DACOSH CACOSH
% Arc hyperbolic tangent arctanh (x) ATANH(X) DATANH CATANH
% Relative error arc (arctan (x) - x) R9ATN1(X) D9ATN1 --
% tangent from first order / x**3
% ***Exponential Integrals and Related Functions***
% Exponential integral Ei(x) = (minus) EI(X) DEI --
% the integral from
% -x to infinity of
% (e**-t / t)dt
% Exponential integral E sub 1 (x) = E1(X) DE1 --
% the integral from x
% to infinity of
% (e**-t / t) dt
% Logarithmic integral li(x) = the ALI(X) DLI --
% integral from 0 to
% x of (1 / ln t) dt
% Sequences of exponential integrals.
% M values are computed where
% k=0,1,...M-1 and n>=1
% Exponential integral E sub n+k (x) Call EXINT(X, DEXINT --
% =the integral from N,KODE,M,TOL,
% 1 to infinity of EN,IERR)
% (e**(-x*t)/t**(n+k))dt
% ***Gamma Functions and Related Functions***
% Factorial n! FAC(N) DFAC --
% Binomial n!/(m!*(n-m)!) BINOM(N,M) DBINOM --
% Gamma gamma(x) GAMMA(X) DGAMMA CGAMMA
% Gamma(x) under and Call GAMLIM( DGAMLM --
% overflow limits XMIN,XMAX)
% Reciprocal gamma 1 / gamma(x) GAMR(X) DGAMR CGAMR
% Log abs gamma ln \gamma(x)\ ALNGAM(X) DLNGAM --
% Log gamma ln gamma(z) -- -- CLNGAM
% Log abs gamma g = ln \gamma(x)\ Call ALGAMS(X, DLGAMS --
% with sign s = sign gamma(x) G,S)
% Incomplete gamma gamma(a,x) = GAMI(A,X) DGAMI --
% the integral from
% 0 to x of
% (t**(a-1) * e**-t)dt
% Complementary gamma(a,x) = GAMIC(A,X) DGAMIC --
% incomplete gamma the integral from
% x to infinity of
% (t**(a-1) * e**-t)dt
% Tricomi's gamma super star(a,x) GAMIT(A,X) DGAMIT --
% incomplete gamma = x**-a *
% incomplete gamma(a,x)
% / gamma(a)
% Psi (Digamma) psi(x) = gamma'(x) PSI(X) DPSI CPSI
% / gamma(x)
% Pochhammer's (a) sub x = gamma(a+x) POCH(A,X) DPOCH --
% generalized symbol / gamma(a)
% Pochhammer's symbol ((a) sub x -1) / x POCH1(A,X) DPOCH1 --
% from first order
% Beta b(a,b) = (gamma(a) BETA(A,B) DBETA CBETA
% * gamma(b))
% / gamma(a+b)
% = the integral
% from 0 to 1 of
% (t**(a-1) *
% (1-t)**(b-1))dt
% Log beta ln b(a,b) ALBETA(A,B) DLBETA CLBETA
% Incomplete beta i sub x (a,b) = BETAI(X,A,B) DBETAI __
% b sub x (a,b) / b(a,b)
% = 1 / b(a,b) *
% the integral
% from 0 to x of
% (t**(a-1) *
% (1-t)**(b-1))dt
% Log gamma correction ln gamma(x) - R9LGMC(X) D9LGMC C9LGMC
% term when Stirling's (ln(2 * pi))/2 -
% approximation is valid (x - 1/2) * ln(x) + x
% ***Error Functions and Fresnel Integrals***
% Error function erf x = (2 / ERF(X) DERF --
% square root of pi) *
% the integral from
% 0 to x of
% e**(-t**2)dt
% Complementary erfc x = (2 / ERFC(X) DERFC --
% error function square root of pi) *
% the integral from
% x to infinity of
% e**(-t**2)dt
% Dawson's function F(x) = e**(-x**2) DAWS(X) DDAWS --
% * the integral from
% from 0 to x of
% e**(t**2)dt
% ***Bessel Functions***
% Bessel functions of special integer order
% First kind, order zero J sub 0 (x) BESJ0(X) DBESJ0 --
% First kind, order one J sub 1 (x) BESJ1(X) DBESJ1 --
% Second kind, order zero Y sub 0 (x) BESY0(X) DBESY0 --
% Second kind, order one Y sub 1 (x) BESY1(X) DBESY1 --
% Modified (hyperbolic) Bessel functions of special integer order
% First kind, order zero I sub 0 (x) BESI0(X) DBESI0 --
% First kind, order one I sub 1 (x) BESI1(X) DBESI1 --
% Third kind, order zero K sub 0 (x) BESK0(X) DBESK0 --
% Third kind, order one K sub 1 (x) BESK1(X) DBESK1 --
% Modified (hyperbolic) Bessel functions of special integer order
% scaled by an exponential
% First kind, order zero e**-\x\ * I sub 0(x) BESI0E(X) DBSI0E --
% First kind, order one e**-\x\ * I sub 1(x) BESI1E(X) DBSI1E --
% Third kind, order zero e**x * K sub 0 (x) BESK0E(X) DBSK0E --
% Third kind, order one e**x * K sub 1 (x) BESK1E(X) DBSK1E --
% Sequences of Bessel functions of general order.
% N values are computed where k = 1,2,...N and v >= 0.
% Modified first kind I sub v+k-1 (x) Call BESI(X, DBESI --
% optional scaling ALPHA,KODE,N,
% by e**(-x) Y,NZ)
% First kind J sub v+k-1 (x) Call BESJ(X, DBESJ --
% ALPHA,N,Y,NZ)
% Second kind Y sub v+k-1 (x) Call BESY(X, DBESY --
% FNU,N,Y)
% Modified third kind K sub v+k-1 (x) Call BESK(X, DBESK --
% optional scaling FNU,KODE,N,Y,
% by e**(x) NZ)
% Sequences of Bessel functions. \N\ values are computed where
% I = 0, 1, 2, ..., N-1 for N > 0 or I = 0, -1, -2, ..., N+1
% for N < 0.
% Modified third kind K sub v+i (x) Call BESKS( DBESKS --
% XNU,X,N,BK)
% Sequences of Bessel functions scaled by an exponential.
% \N\ values are computed where I = 0, 1, 2, ..., N-1
% for N > 0 or I = 0, -1, -2, ..., N+1 for N < 0.
% Modified third kind e**x * Call BESKES( DBSKES --
% K sub v+i (x) XNU,X,N,BK)
% ***Bessel Functions of Fractional Order***
% Airy functions
% Airy Ai(x) AI(X) DAI --
% Bairy Bi(x) BI(X) DBI --
% Exponentially scaled Airy functions
% Airy Ai(x), x <= 0 AIE(X) DAIE --
% exp(2/3 * x**(3/2))
% * Ai(x), x >= 0
% Bairy Bi(x), x <= 0 BIE(X) DBIE --
% exp(-2/3 * x**(3/2))
% * Bi(x), x >= 0
% ***Confluent Hypergeometric Functions***
% Confluent U(a,b,x) CHU(A,B,X) DCHU --
% hypergeometric
% ***Miscellaneous Functions***
% Spence s(x) = - the SPENC(X) DSPENC --
% dilogarithm integral from
% 0 to x of
% ((ln \1-y\) / y)dy
%
%***REFERENCES (NONE)
%***ROUTINES CALLED (NONE)
%***REVISION HISTORY (YYMMDD)
% 801015 DATE WRITTEN
% 861211 REVISION DATE from Version 3.2
% 891214 Prologue converted to Version 4.0 format. (BAB)
% 900326 Routine name changed from FNLIBD to FUNDOC. (WRB)
% 900723 PURPOSE section revised. (WRB)
%***end PROLOGUE FUNDOC
%***FIRST EXECUTABLE STATEMENT FUNDOC
end
%DECK FZERO
