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. . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!