This book contains tables of integrals of the Mellin
transform type
Since the substitution x = e transforms (a) into
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-
Particularly 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 cj> (x) by (a)
is known, then $(z) belonging to x (x) or more general to
x cj> (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 concerning Mellin trans-
transforms 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.