SLATEC Common Mathematical Library -- Table of Contents


SECTION I. User-callable Routines
Category C. Elementary and special functions (search also class L5)

         C1.  Integer-valued functions 
         C2.  Powers, roots, reciprocals
         C3.  Polynomials
         C4.  Elementary transcendental functions
         C5.  Exponential and logarithmic integrals
         C7.  Gamma
         C8.  Error functions
         C9.  Legendre functions
         C10.  Bessel functions
         C11.  Confluent hypergeometric functions
         C14.  Elliptic integrals
         C19.  Other special functions
 
          FUNDOC-A  Documentation for FNLIB, a collection of routines for
                    evaluating elementary and special functions.
 
C1.  Integer-valued functions (e.g., floor, ceiling, factorial, binomial
     coefficient)
 
          BINOM-S   Compute the binomial coefficients.
          DBINOM-D
 
          FAC-S     Compute the factorial function.
          DFAC-D
 
          POCH-S    Evaluate a generalization of Pochhammer's symbol.
          DPOCH-D
 
          POCH1-S   Calculate a generalization of Pochhammer's symbol starting
          DPOCH1-D  from first order.
 
C2.  Powers, roots, reciprocals
 
          CBRT-S    Compute the cube root.
          DCBRT-D
          CCBRT-C
 
C3.  Polynomials
C3A.  Orthogonal
C3A2.  Chebyshev, Legendre
 
          CSEVL-S   Evaluate a Chebyshev series.
          DCSEVL-D
 
          INITS-S   Determine the number of terms needed in an orthogonal
          INITDS-D  polynomial series so that it meets a specified accuracy.
 
          QMOMO-S   This routine computes modified Chebyshev moments.  The K-th
          DQMOMO-D  modified Chebyshev moment is defined as the integral over
                    (-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev
                    polynomial of degree K.
 
          XLEGF-S   Compute normalized Legendre polynomials and associated
          DXLEGF-D  Legendre functions.
 
          XNRMP-S   Compute normalized Legendre polynomials.
          DXNRMP-D
 
C4.  Elementary transcendental functions
C4A.  Trigonometric, inverse trigonometric
 
          CACOS-C   Compute the complex arc cosine.
 
          CASIN-C   Compute the complex arc sine.
 
          CATAN-C   Compute the complex arc tangent.
 
          CATAN2-C  Compute the complex arc tangent in the proper quadrant.
 
          COSDG-S   Compute the cosine of an argument in degrees.
          DCOSDG-D
 
          COT-S     Compute the cotangent.
          DCOT-D
          CCOT-C
 
          CTAN-C    Compute the complex tangent.
 
          SINDG-S   Compute the sine of an argument in degrees.
          DSINDG-D
 
C4B.  Exponential, logarithmic
 
          ALNREL-S  Evaluate ln(1+X) accurate in the sense of relative error.
          DLNREL-D
          CLNREL-C
 
          CLOG10-C  Compute the principal value of the complex base 10
                    logarithm.
 
          EXPREL-S  Calculate the relative error exponential (EXP(X)-1)/X.
          DEXPRL-D
          CEXPRL-C
 
C4C.  Hyperbolic, inverse hyperbolic
 
          ACOSH-S   Compute the arc hyperbolic cosine.
          DACOSH-D
          CACOSH-C
 
          ASINH-S   Compute the arc hyperbolic sine.
          DASINH-D
          CASINH-C
 
          ATANH-S   Compute the arc hyperbolic tangent.
          DATANH-D
          CATANH-C
 
          CCOSH-C   Compute the complex hyperbolic cosine.
 
          CSINH-C   Compute the complex hyperbolic sine.
 
          CTANH-C   Compute the complex hyperbolic tangent.
 
C5.  Exponential and logarithmic integrals
 
          ALI-S     Compute the logarithmic integral.
          DLI-D
 
          E1-S      Compute the exponential integral E1(X).
          DE1-D
 
          EI-S      Compute the exponential integral Ei(X).
          DEI-D
 
          EXINT-S   Compute an M member sequence of exponential integrals
          DEXINT-D  E(N+K,X), K=0,1,...,M-1 for N .GE. 1 and X .GE. 0.
 
          SPENC-S   Compute a form of Spence's integral due to K. Mitchell.
          DSPENC-D
 
C7.  Gamma
C7A.  Gamma, log gamma, reciprocal gamma
 
          ALGAMS-S  Compute the logarithm of the absolute value of the Gamma
          DLGAMS-D  function.
 
          ALNGAM-S  Compute the logarithm of the absolute value of the Gamma
          DLNGAM-D  function.
          CLNGAM-C
 
          C0LGMC-C  Evaluate (Z+0.5)*LOG((Z+1.)/Z) - 1.0 with relative
                    accuracy.
 
          GAMLIM-S  Compute the minimum and maximum bounds for the argument in
          DGAMLM-D  the Gamma function.
 
          GAMMA-S   Compute the complete Gamma function.
          DGAMMA-D
          CGAMMA-C
 
          GAMR-S    Compute the reciprocal of the Gamma function.
          DGAMR-D
          CGAMR-C
 
          POCH-S    Evaluate a generalization of Pochhammer's symbol.
          DPOCH-D
 
          POCH1-S   Calculate a generalization of Pochhammer's symbol starting
          DPOCH1-D  from first order.
 
C7B.  Beta, log beta
 
          ALBETA-S  Compute the natural logarithm of the complete Beta
          DLBETA-D  function.
          CLBETA-C
 
          BETA-S    Compute the complete Beta function.
          DBETA-D
          CBETA-C
 
C7C.  Psi function
 
          PSI-S     Compute the Psi (or Digamma) function.
          DPSI-D
          CPSI-C
 
          PSIFN-S   Compute derivatives of the Psi function.
          DPSIFN-D
 
C7E.  Incomplete gamma
 
          GAMI-S    Evaluate the incomplete Gamma function.
          DGAMI-D
 
          GAMIC-S   Calculate the complementary incomplete Gamma function.
          DGAMIC-D
 
          GAMIT-S   Calculate Tricomi's form of the incomplete Gamma function.
          DGAMIT-D
 
C7F.  Incomplete beta
 
          BETAI-S   Calculate the incomplete Beta function.
          DBETAI-D
 
C8.  Error functions
C8A.  Error functions, their inverses, integrals, including the normal
      distribution function
 
          ERF-S     Compute the error function.
          DERF-D
 
          ERFC-S    Compute the complementary error function.
          DERFC-D
 
C8C.  Dawson's integral
 
          DAWS-S    Compute Dawson's function.
          DDAWS-D
 
C9.  Legendre functions
 
          XLEGF-S   Compute normalized Legendre polynomials and associated
          DXLEGF-D  Legendre functions.
 
          XNRMP-S   Compute normalized Legendre polynomials.
          DXNRMP-D
 
C10.  Bessel functions
C10A.  J, Y, H-(1), H-(2)
C10A1.  Real argument, integer order
 
          BESJ0-S   Compute the Bessel function of the first kind of order
          DBESJ0-D  zero.
 
          BESJ1-S   Compute the Bessel function of the first kind of order one.
          DBESJ1-D
 
          BESY0-S   Compute the Bessel function of the second kind of order
          DBESY0-D  zero.
 
          BESY1-S   Compute the Bessel function of the second kind of order
          DBESY1-D  one.
 
C10A3.  Real argument, real order
 
          BESJ-S    Compute an N member sequence of J Bessel functions
          DBESJ-D   J/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA
                    and X.
 
          BESY-S    Implement forward recursion on the three term recursion
          DBESY-D   relation for a sequence of non-negative order Bessel
                    functions Y/SUB(FNU+I-1)/(X), I=1,...,N for real, positive
                    X and non-negative orders FNU.
 
C10A4.  Complex argument, real order
 
          CBESH-C   Compute a sequence of the Hankel functions H(m,a,z)
          ZBESH-C   for superscript m=1 or 2, real nonnegative orders a=b,
                    b+1,... where b>0, and nonzero complex argument z.  A
                    scaling option is available to help avoid overflow.
 
          CBESJ-C   Compute a sequence of the Bessel functions J(a,z) for
          ZBESJ-C   complex argument z and real nonnegative orders a=b,b+1,
                    b+2,... where b>0.  A scaling option is available to
                    help avoid overflow.
 
          CBESY-C   Compute a sequence of the Bessel functions Y(a,z) for
          ZBESY-C   complex argument z and real nonnegative orders a=b,b+1,
                    b+2,... where b>0.  A scaling option is available to
                    help avoid overflow.
 
C10B.  I, K
C10B1.  Real argument, integer order
 
          BESI0-S   Compute the hyperbolic Bessel function of the first kind
          DBESI0-D  of order zero.
 
          BESI0E-S  Compute the exponentially scaled modified (hyperbolic)
          DBSI0E-D  Bessel function of the first kind of order zero.
 
          BESI1-S   Compute the modified (hyperbolic) Bessel function of the
          DBESI1-D  first kind of order one.
 
          BESI1E-S  Compute the exponentially scaled modified (hyperbolic)
          DBSI1E-D  Bessel function of the first kind of order one.
 
          BESK0-S   Compute the modified (hyperbolic) Bessel function of the
          DBESK0-D  third kind of order zero.
 
          BESK0E-S  Compute the exponentially scaled modified (hyperbolic)
          DBSK0E-D  Bessel function of the third kind of order zero.
 
          BESK1-S   Compute the modified (hyperbolic) Bessel function of the
          DBESK1-D  third kind of order one.
 
          BESK1E-S  Compute the exponentially scaled modified (hyperbolic)
          DBSK1E-D  Bessel function of the third kind of order one.
 
C10B3.  Real argument, real order
 
          BESI-S    Compute an N member sequence of I Bessel functions
          DBESI-D   I/SUB(ALPHA+K-1)/(X), K=1,...,N or scaled Bessel functions
                    EXP(-X)*I/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative
                    ALPHA and X.
 
          BESK-S    Implement forward recursion on the three term recursion
          DBESK-D   relation for a sequence of non-negative order Bessel
                    functions K/SUB(FNU+I-1)/(X), or scaled Bessel functions
                    EXP(X)*K/SUB(FNU+I-1)/(X), I=1,...,N for real, positive
                    X and non-negative orders FNU.
 
          BESKES-S  Compute a sequence of exponentially scaled modified Bessel
          DBSKES-D  functions of the third kind of fractional order.
 
          BESKS-S   Compute a sequence of modified Bessel functions of the
          DBESKS-D  third kind of fractional order.
 
C10B4.  Complex argument, real order
 
          CBESI-C   Compute a sequence of the Bessel functions I(a,z) for
          ZBESI-C   complex argument z and real nonnegative orders a=b,b+1,
                    b+2,... where b>0.  A scaling option is available to
                    help avoid overflow.
 
          CBESK-C   Compute a sequence of the Bessel functions K(a,z) for
          ZBESK-C   complex argument z and real nonnegative orders a=b,b+1,
                    b+2,... where b>0.  A scaling option is available to
                    help avoid overflow.
 
C10D.  Airy and Scorer functions
 
          AI-S      Evaluate the Airy function.
          DAI-D
 
          AIE-S     Calculate the Airy function for a negative argument and an
          DAIE-D    exponentially scaled Airy function for a non-negative
                    argument.
 
          BI-S      Evaluate the Bairy function (the Airy function of the
          DBI-D     second kind).
 
          BIE-S     Calculate the Bairy function for a negative argument and an
          DBIE-D    exponentially scaled Bairy function for a non-negative
                    argument.
 
          CAIRY-C   Compute the Airy function Ai(z) or its derivative dAi/dz
          ZAIRY-C   for complex argument z.  A scaling option is available
                    to help avoid underflow and overflow.
 
          CBIRY-C   Compute the Airy function Bi(z) or its derivative dBi/dz
          ZBIRY-C   for complex argument z.  A scaling option is available
                    to help avoid overflow.
 
C10F.  Integrals of Bessel functions
 
          BSKIN-S   Compute repeated integrals of the K-zero Bessel function.
          DBSKIN-D
 
C11.  Confluent hypergeometric functions
 
          CHU-S     Compute the logarithmic confluent hypergeometric function.
          DCHU-D
 
C14.  Elliptic integrals
 
          RC-S      Calculate an approximation to
          DRC-D      RC(X,Y) = Integral from zero to infinity of
                                      -1/2     -1
                            (1/2)(t+X)    (t+Y)  dt,
                    where X is nonnegative and Y is positive.
 
          RD-S      Compute the incomplete or complete elliptic integral of the
          DRD-D     2nd kind.  For X and Y nonnegative, X+Y and Z positive,
                     RD(X,Y,Z) = Integral from zero to infinity of
                                        -1/2     -1/2     -3/2
                              (3/2)(t+X)    (t+Y)    (t+Z)    dt.
                    If X or Y is zero, the integral is complete.
 
          RF-S      Compute the incomplete or complete elliptic integral of the
          DRF-D     1st kind.  For X, Y, and Z non-negative and at most one of
                    them zero, RF(X,Y,Z) = Integral from zero to infinity of
                                        -1/2     -1/2     -1/2
                              (1/2)(t+X)    (t+Y)    (t+Z)    dt.
                    If X, Y or Z is zero, the integral is complete.
 
          RJ-S      Compute the incomplete or complete (X or Y or Z is zero)
          DRJ-D     elliptic integral of the 3rd kind.  For X, Y, and Z non-
                    negative, at most one of them zero, and P positive,
                     RJ(X,Y,Z,P) = Integral from zero to infinity of
                                          -1/2     -1/2     -1/2     -1
                                (3/2)(t+X)    (t+Y)    (t+Z)    (t+P)  dt.
 
C19.  Other special functions
 
          RC3JJ-S   Evaluate the 3j symbol f(L1) = (  L1   L2 L3)
          DRC3JJ-D                                 (-M2-M3 M2 M3)
                    for all allowed values of L1, the other parameters
                    being held fixed.
 
          RC3JM-S   Evaluate the 3j symbol g(M2) = (L1 L2   L3  )
          DRC3JM-D                                 (M1 M2 -M1-M2)
                    for all allowed values of M2, the other parameters
                    being held fixed.
 
          RC6J-S    Evaluate the 6j symbol h(L1) = {L1 L2 L3}
          DRC6J-D                                  {L4 L5 L6}
                    for all allowed values of L1, the other parameters
                    being held fixed.