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

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		*           DISK TO ACCOMPANY          *
		*   COMPUTATION OF SPECIAL FUNCTIONS   *
		*                                      *
		*   Shanjie Zhang and Jianming Jin     *
		*                                      *
		*   Copyright 1996 by John Wiley &     *
		*              Sons, Inc.              *
		*                                      *
		****************************************

The Fortran 90 version of these functions is by Alan Miller.
e-mail: amiller @ bigpond.net.au
web:    http://users.bigpond.net.au/amiller

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: [e-mail]) 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 jinds
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