An Algorithmic Approach to the Mellin Transform Method

Karen T. Kohl; Flavia Iulia Stan

An Algorithmic Approach to the Mellin Transform Method

Karen T. Kohl, Flavia Iulia Stan

Research Institute for Symbolic Computation

Research output: Working paper and reports › Research report

Abstract

We present proofs for typical entries from the Gradshteyn-Ryzhik Table of Integrals using the Mellin transform method and computer algebra algorithms based on WZ theory. After representing an identity from the Table in terms of multiple contour integrals of Barnes' type and nested sums, we use Wegschaider's summation algorithm to find recurrences satisfied by both sides of this identity and check finitely many initial values.

Original language	English
Place of Publication	JKU Linz, Altenberger Straße 69, 4040 Linz
Publisher	DK, JKU Linz
Number of pages	1
Publication status	Published - Nov 2009

Publication series

Name	DK Report Series
No.	2009-03

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

Cite this

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abstract = "We present proofs for typical entries from the Gradshteyn-Ryzhik Table of Integrals using the Mellin transform method and computer algebra algorithms based on WZ theory. After representing an identity from the Table in terms of multiple contour integrals of Barnes' type and nested sums, we use Wegschaider's summation algorithm to find recurrences satisfied by both sides of this identity and check finitely many initial values.",

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N2 - We present proofs for typical entries from the Gradshteyn-Ryzhik Table of Integrals using the Mellin transform method and computer algebra algorithms based on WZ theory. After representing an identity from the Table in terms of multiple contour integrals of Barnes' type and nested sums, we use Wegschaider's summation algorithm to find recurrences satisfied by both sides of this identity and check finitely many initial values.

AB - We present proofs for typical entries from the Gradshteyn-Ryzhik Table of Integrals using the Mellin transform method and computer algebra algorithms based on WZ theory. After representing an identity from the Table in terms of multiple contour integrals of Barnes' type and nested sums, we use Wegschaider's summation algorithm to find recurrences satisfied by both sides of this identity and check finitely many initial values.

M3 - Research report

T3 - DK Report Series

BT - An Algorithmic Approach to the Mellin Transform Method

PB - DK, JKU Linz

CY - JKU Linz, Altenberger Straße 69, 4040 Linz

ER -