Tables of Mellin Transforms

Released on by F. Oberhettinger
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  • Tables of Mellin Transforms Book Detail

  • Author : F. Oberhettinger
  • Release Date : 2012-12-06
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 284
  • ISBN 13 : 3642659756
  • File Size : 73,73 MB
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Tables of Mellin Transforms by F. Oberhettinger PDF Summary

Book Description: 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Tables of Mellin Transforms

Tables of Mellin Transforms

File Size : 39,39 MB
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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)

Handbook of Mellin Transforms

Handbook of Mellin Transforms

File Size : 11,11 MB
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The Mellin transformation is widely used in various problems of pure and applied mathematics, in particular, in the theory of differential and integral equation

Table of Integrals, Series, and Products

Table of Integrals, Series, and Products

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The Table of Integrals, Series, and Products is the essential reference for integrals in the English language. Mathematicians, scientists, and engineers, rely o