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ACM SIGSAM Bulletin, 1989
This article describes a method by which the integration capabilities of symbolic-mathematics computer programs can be extended to include integrals that contain special functions. A summary of the theory that forms the basis of the method is given in Appendix A. A few integrals that have been evaluated using the method are presented in Appendix B.
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This article describes a method by which the integration capabilities of symbolic-mathematics computer programs can be extended to include integrals that contain special functions. A summary of the theory that forms the basis of the method is given in Appendix A. A few integrals that have been evaluated using the method are presented in Appendix B.
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2006
This is an overview article on q-special functions, a slightly extended version of an article to appear in the Encyclopedia of Mathematical Physics, Elsevier, 2006.
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This is an overview article on q-special functions, a slightly extended version of an article to appear in the Encyclopedia of Mathematical Physics, Elsevier, 2006.
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Validated Special Functions Software
2010Because of the importance of special functions, several books and a large collection of papers have been devoted to the numerical computation of these functions, the most well-known being the NBS handbook by Abramowitz and Stegun. But up to this date, symbolic and numeric environments offer no routines for the validated evaluation of special functions.
Cuyt, Annie +3 more
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Integration of Liouvillian functions with special functions
Proceedings of the fifth ACM symposium on Symbolic and algebraic computation - SYMSAC '86, 1986In this paper, we discuss a decision procedure for the indefinite integration of transcendental Liouvillian functions in terms of elementary functions and logarithmic integrals. We also discuss a decision procedure for the integration of a large class of transcendental Liouvillian functions in terms of elementary functions and error-functions.
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Lobachevskii Journal of Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Special Function Field Sieve
SIAM Journal on Discrete Mathematics, 2002Summary: Let \(p\) be a prime number and \(n\) a positive integer, and let \(q=p^{n}\). \textit{L. M. Adleman} and \textit{M.-D. A. Huang} [Inf. Comput. 151, 5--16 (1999; Zbl 1006.11078)] described a version of the function field sieve which is conjectured to compute a logarithm in the field of \(q\) elements in expected time \(L_{q}[1/3;(32/9)^{1/3}+o(
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2010
The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original ...
Richard Beals, Roderick Wong
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The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original ...
Richard Beals, Roderick Wong
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1994
Abstract It is strongly suggested by the generalized binomial expansion of Chapter XII that a multivariable version of the hypergeometric function can be associated with every symmetric cone. The theory of these functions is the subject of the present chapter. After proving some general results we look in more detail at the special cases
Jacques Faraut, Adam Korányi
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Abstract It is strongly suggested by the generalized binomial expansion of Chapter XII that a multivariable version of the hypergeometric function can be associated with every symmetric cone. The theory of these functions is the subject of the present chapter. After proving some general results we look in more detail at the special cases
Jacques Faraut, Adam Korányi
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