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 c(z) corresponding to a given q,(x) by (a) is known, then c(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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
- ISBN13 9783540069423
- Publish Date 29 November 1974
- Publish Status Active
- Publish Country DE
- Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Edition Softcover reprint of the original 1st ed. 1974
- Format Paperback
- Pages 278
- Language English