Tables of Mellin Transforms

• Fritz Oberhettinger
Book

1. Front Matter
Pages i-v
2. Mellin Transforms

1. Fritz Oberhettinger
Pages 1-5
2. Fritz Oberhettinger
Pages 6-162
3. Inverse Mellin Transforms

1. Fritz Oberhettinger
Pages 163-258
4. Back Matter
Pages 259-278

Introduction

This book contains tables of integrals of the Mellin transform type z-l J (a) 1> (z) q,(x)x dx o t Since the substitution x = e- transforms (a) into (b) 1> (z) the Mellin transform is sometimes referred to as the two sided Laplace transform. The use of the Mellin transform in various problems in mathematical analysis is well established. Parti­ cularly widespread and effective is its application to problems arising in analytic number theory. This is partially due to the fact that if ¢(z) corresponding to a given q,(x) by (a) is known, then ¢(z) belonging to xaq,(x) or more general to P xaq,(x ) (p real) is likewise known. (See particularly the rules in sections 1. 1 and 2. 1 of this book. ) A list of major contributions conce~ning Mellin trans­ forms is added at the end of the introduction. Latin letters (unless otherwise stated) denote real positive numbers while Greek letters denote complex parameters within the given range of validity. The author is indebted to Mrs. Jolan Eross for her tireless effort and patience while typing this manuscript. Oregon State University Corvallis, Oregon May 1974 Fritz Oberhettinger Contents Part I. Mellin Transforms Introduction. . . • . • • • . • . . . . . . . . . . . . • • • • . . . • . • . . • • • . • . 1 Some Applications of the Mellin Transform Analysis. ••. •••. . . •. •. . . . •• . • . . . . . . ••. . . . . •• 6 1. 1 General Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1. 2 Algebraic Functions and Powers of Arbitrary Order . . . 13 1. 3 Exponential Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Keywords

Bessel-Funktion Koordinatentransformation Mellin-Transformation elliptic function integral logarithm mathematical analysis orthogonal polynomials

Authors and affiliations

• Fritz Oberhettinger
• 1
1. 1.Oregon State UniversityCorvallisUSA

Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-65975-1
• Copyright Information Springer-Verlag Berlin Heidelberg 1974
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-540-06942-3
• Online ISBN 978-3-642-65975-1