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This material represents a collection of integrals of the Laplace-
and inverse Laplace Transform type. The usef- ness of this kind of
information as a tool in various branches of Mathematics is firmly
established. Previous publications include the contributions by A.
Erdelyi and Roberts and Kaufmann (see References). Special
consideration is given to results involving higher functions as
integrand and it is believed that a substantial amount of them is
presented here for the first time. Greek letters denote complex
parameters within the given range of validity. Latin letters denote
(unless otherwise stated) real positive parameters and a possible
extension to complex values by analytic continuation will often
pose no serious problem. The authors are indebted to Mrs. Jolan
Eross for her tireless effort and patience while typing this manu
script. Oregon State University Corvallis, Oregon Eastern Michigan
University Ypsilanti, Michigan The Authors Contents Part I. Laplace
Transforms In troduction. . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 1 1. 1 General Formulas.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1. 2 Algebraic Functions. . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 12 1. 3 Powers of Arbitrary Order. . . . . . . . .
. . . . . . . . . . . . . . . 21 1. 4 Sectionally Rational- and
Rows of Delta Functions 28 1. 5 Exponential Functions. . . . . . .
. . . . . . . . . . . . . . . . . . . . . 37 1. 6 Logarithmic
Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
1. 7 Trigonometric Functions. . . . . . . . . . . . . . . . . . . .
. . . . . . 54 1. 8 Inverse Trigonometric Functions. . . . . . . .
. . . . . . . . . . 81 1. 9 Hyperbolic Functions. . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 84 1. 10 Inverse Hyperbolic
Functions. . . . . . . . . . . . . . . . . . . . . 99 1. 11
Orthogonal Polynomials . . . . . . . . . . . . . . . . . . . . . .
. . . . 103 1. 12 Legendre Functions . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 113 1. 13 Bessel Functions of Order
Zero and Unity . . . . . . . . . 119 1. 14 Bessel Functions. . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 1. 15
Modified Bessel Functions . . . . . . . . . . . . . . . . . . . . .
. . ."
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