Deals with the automatic computation of special functions which appear in all areas of engineering and the physical sciences. Contains over 100 computer programs written by the authors and describes the algorithms to provide readers with specific information about each individual program. Consisting of three sections, the first one presents an introduction to the special function to be dealt with, its major properties, and several formulas needed for its computation. The second segment features algorithms for computing the special function and the related quantities and lists corresponding Fortran-77 programs. The final part tabulates representative results to offer a quick outlook on the function's behavior and to check the computed results. The accompanying disk contains all the computer programs discussed in the text.
Abel , N. H. , 14 , 106 , 600 , 605 Adams , J. C. , 320 Agarwal , R. P. , 586 Ahern , P. , 36 Airy , G. B. , 201 Al ... 185 , 277 , 319 , 386 , 398 , 400 Bak , J. , 306 Barnes , E. W. , 61 Bateman , H. , 277 , 313 , 314 , 475 Baxter ...
Additionally, we observe that the generalized Laguerre weight function with parameter a I —1/6 appears explicitly in the integrand and that the additional factor f(t) I (1 + t/O'l/6 has small derivatives when |Z| is large; therefore, ...
Contains the various principal special functions in common use and their basic properties and manipulations.
Calculation of Special Functions: The Gamma Function, the Exponential Integrals and Error-like Functions
This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems.
When we look at Kummer's equation ( 7.4 ) we see that the Laguerre polynomial is a 1F1 - function : Ln ( x ) = ( " + a ) n 1F1 ( -n ; a + 1 ; v ) , where the binomial coefficient is chosen for normalization and on account of convention ...
These are the proceedings of the conference "Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics" held at the Department of Mathematics, University of Florida, Gainesville, from November 11 to 13, 1999.
... A. Guionnet & O. Zeitouni An introduction to random matrices 119 C. Perez-Garcia & W. H. Schikhof Locally convex spaces over non-Archimedean valued fields 120 P. K. Friz & N. B. Victoir Multidimensional stochastic processes as rough ...
The subject of this book is the theory of special functions, not considered as a list of functions exhibiting a certain range of properties, but based on the unified study of singularities of second-order ordinary differential equations in ...
The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions.