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mairya.for (8286, 1998-02-06)
mairyb.for (5591, 1998-02-06)
mairyzo.for (9942, 1998-02-06)
maswfa.for (10992, 1998-02-06)
maswfb.for (10748, 1998-02-06)
mbernoa.for (1757, 1998-02-06)
mbernob.for (1829, 1998-02-06)
mbeta.for (3324, 1998-02-06)
mcchg.for (6720, 1998-02-06)
mcerror.for (2244, 1998-02-06)
mcerzo.for (4842, 1998-02-06)
mcgama.for (4381, 1998-02-06)
mch12n.for (13830, 1998-02-06)
mchgm.for (5881, 1998-02-06)
mchgu.for (16742, 1998-02-06)
mcik01.for (6305, 1998-02-06)
mciklv.for (4629, 1998-02-06)
mcikna.for (11404, 1998-02-06)
mciknb.for (8205, 1998-02-06)
mcikva.for (12138, 1998-02-06)
mcikvb.for (11785, 1998-02-06)
mcisia.for (3544, 1998-02-06)
mcisib.for (2502, 1998-02-06)
mcjk.for (1930, 1998-02-06)
mcjy01.for (7485, 1998-02-06)
mcjylv.for (4674, 1998-02-06)
mcjyna.for (15643, 1998-02-06)
mcjynb.for (10859, 1998-02-06)
mcjyva.for (14965, 1998-02-06)
mcjyvb.for (11944, 1998-02-06)
mclpmn.for (4600, 1998-02-06)
mclpn.for (2834, 1998-02-06)
mclqmn.for (5860, 1998-02-06)
mclqn.for (4074, 1998-02-06)
mcomelp.for (2239, 1998-02-06)
mcpbdn.for (6726, 1998-02-06)
mcpsi.for (3329, 1998-02-06)
mcsphik.for (7355, 1998-02-06)
mcsphjy.for (7392, 1998-02-06)
mcva1.for (7052, 1998-02-06)
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**************************************** * DISK TO ACCOMPANY * * COMPUTATION OF SPECIAL FUNCTIONS * * * * Shanjie Zhang and Jianming Jin * * * * Copyright 1996 by John Wiley & * * Sons, Inc. * * * **************************************** I. INTRODUCTION As stated in the preface of our book "Computation of Special Functions," the purpose of this book is to share with the reader a set of computer programs (130 in total) which we have developed during the past several years for computing a variety of special mathematical functions. For your convenience, we attach to the book this diskette that contains all the computer programs listed or mentioned in the book. In this diskette, we place all the programs under directory SMF\PROGRAMS. In order to illustrate the use of these programs and facilitate your testing of the programs, we wrote a short simple main program for each program so that you can readily test them. All the programs are written in FORTRAN-77 and tested on PCs and workstations. Therefore, they should run on any computer with implementation of the FORTRAN-77 standard. Although we have made a great effort to test these programs, we would not be surprised to find some errors in them. We would appreciate it if you can bring to our attention any errors you find. You can do this by either writing us directly at the location (e-mail: j-jin1@uiuc.edu) or writing to the publisher, whose address appears on the back cover of the book. However, we must note that all these programs are sold "as is," and we cannot guarantee to correct the errors reported by readers on any fixed schedule. All the programs and subroutines contained in this diskette are copyrighted. However, we give permission to the reader who purchases this book to incorporate any of these programs into his or her programs provided that the copyright is acknowledged. Regarding the specifics of the programs, we want to make the following two points. 1) All the programs are written in double precision. Although the use of double precision is necessary for some programs, especially for those based on series expansions, it is not necessary for all programs. For example, the computation of of special functions based on polynomial approximations does not have to use double precision. We chose to write all the programs using double precision in order to avoid possible confusion which may occur in using these programs. If necessary, you can convert the programs into the single precision format easily. However, doing so for some programs may lead to a lower accuracy. 2) In the main programs that calculate a sequence of special functions, we usually set the maximum order or degree to 100 or 250. However, this is not a limit. To compute functions with a higher order or degree, all you need to do is simply set the dimension of proper arrays higher. II. DISCLAIMER OF WARRANTY Although we have made a great effort to test and validate the computer programs, we make no warranties, express or implied, that these programs are free of error, or are consistent with any particular standard of merchantability, or that they will meet your requirements for any particular application. They should not be relied on for solving problems whose incorrect solution could result in injury to a person or loss of property. If you do use the programs in such a manner, it is at your own risk. The authors and publisher disclaim all liability for direct or consequential damages resulting from your use of the programs. III. LIST OF PROGRAMS (Please note that all file names of programs installed from the disk begin with an M, for example, MBERNOA.FOR) BERNOA Evaluate a sequence of Bernoulli numbers (method 1). BERNOB Evaluate a sequence of Bernoulli numbers (method 2). EULERA Evaluate a sequence of Euler numbers (method 1). EULERB Evaluate a sequence of Euler numbers (method 2). ***** OTHPL Evaluate a sequence of orthogonal polynomials and their derivatives, including Chebyshev, Laguerre, and Hermite polynomials. LEGZO Evaluate the nodes and weights for Gauss-Legendre quadrature. LAGZO Evaluate the nodes and weights for Gauss-Laguerre quadrature. HERZO Evaluate the nodes and weights for Gauss-Hermite quadrature. ***** GAMMA Evaluate the gamma function. LGAMA Evaluate the gamma function or the logarithm of the gamma function. CGAMA Evaluate the gamma function with a complex argument. BETA Evaluate the beta function. PSI Evaluate the psi function. CPSI Evaluate the psi function with a complex argument. INCOG Evaluate the incomplete gamma function. INCOB Evaluate the incomplete beta function. ***** LPN Evaluate a sequence of Legendre polynomials and their derivatives with real arguments. CLPN Evaluate a sequence of Legendre polynomials and their derivatives with complex arguments. LPNI Evaluate a sequence of Legendre polynomials, their derivatives, and their integrals. LQNA Evaluate a sequence of Legendre functions of the second kind and their derivatives with restricted real arguments. LQNB Evaluate a sequence of Legendre functions of the second kind and their derivatives with nonrestricted real arguments. CLQN Evaluate a sequence of Legendre functions of the second kind and their derivatives with complex arguments. LPMN Evaluate a sequence of associated Legendre polynomials and their derivatives with real arguments. CLPMN Evaluate a sequence of associated Legendre polynomials and their derivatives with complex arguments. LQMN Evaluate a sequence of associated Legendre functions of the second kind and their derivatives with real arguments. CLQMN Evaluate a sequence of associated Legendre functions of the second kind and their derivatives with complex arguments. LPMV Evaluate associated Legendre functions of the first kind with an integer order and arbitrary non-negative degree. ***** JY01A Evaluate the zeroth- and first-order Bessel functions of the first and second kinds with real arguments using series and asymptotic expansions. JY01B Evaluate the zeroth- and first-order Bessel functions of the first and second kinds with real arguments using polynomial approximations. JYNA Evaluate a sequence of Bessel functions of the first and second kinds and their derivatives with integer orders and real arguments (method 1). JYNB Evaluate a sequence of Bessel functions of the first and second kinds and their derivatives with integer orders and real arguments (method 2). CJY01 Evaluate the zeroth- and first-order Bessel functions of the first and second kinds and their derivatives with complex arguments. CJYNA Evaluate a sequence of Bessel functions of the first and second kinds and their derivatives with integer orders and complex arguments (method 1). CJYNB Evaluate a sequence of Bessel functions of the first and second kinds and their derivatives with integer orders and complex arguments (method 2). JYV Evaluate a sequence of Bessel functions of the first and second kinds and their derivatives with arbitrary real orders and real arguments. CJYVA Evaluate a sequence of Bessel functions of the first and second kinds and their derivatives with arbitrary real orders and complex arguments (method 1). CJYVB Evaluate a sequence of Bessel functions of the first and second kinds and their derivatives with arbitrary real orders and complex arguments (method 2). CJK Evaluate the coefficients for the asymptotic expansion of Bessel functions for large orders. CJYLV Evaluate Bessel functions of the first and second kinds and their derivatives with a large arbitrary real order and complex arguments. JYZO Evaluate the zeros of the Bessel functions of the first and second kinds and their derivatives. JDZO Evaluate the zeros of the Bessel functions of the first kind and their derivatives. CYZO Evaluate the complex zeros of the Bessel functions of the second kind of order zero and one. LAMN Evaluate a sequence of lambda functions with integer orders and their derivatives. LAMV Evaluate a sequence of lambda functions with arbitrary orders and their derivatives. ***** IK01A Evaluate the zeroth- and first-order modified Bessel functions of the first and second kinds with real arguments. IK01B Evaluate the zeroth- and first-order modified Bessel functions of the first and second kinds with real arguments. IKNA Evaluate a sequence of modified Bessel functions of the first and second kinds and their derivatives with integer orders and real arguments (method 1). IKNB Evaluate a sequence of modified Bessel functions of the first and second kinds and their derivatives with integer orders and real arguments (method 2). CIK01 Evaluate the zeroth- and first-order modified Bessel functions of the first and second kinds and their derivatives with complex arguments. CIKNA Evaluate a sequence of modified Bessel functions of the first and second kinds and their derivatives with integer orders and complex arguments (method 1). CIKNB Evaluate a sequence of modified Bessel functions of the first and second kinds and their derivatives with integer orders and complex arguments (method 2). IKV Evaluate a sequence of modified Bessel functions of the first and 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).

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