This material represents a collection of integral tra- forms involving Bessel (or related) functions as kernel. The following types of inversion formulas have been singled out. k I. g(y) = f (x) (xy) 2J (xy) dx J V 0 k I' . f (x) g (y) (xy) 2J (xy) dy J V 0 II. g(y) f(x) (XY)~K (xy)dx J v 0 c+ioo k 1 II'. f (x) = g (y) (xy) 2 [Iv (xy) + I_v(xy)]dy J 27fT c-ioo or also c+ioo k 1 II". f(x) = g (y) (xy) 2Iv (xy) dx J rri oo c-i k III. g(y) f(x) (xy) 2y (xy) dx + J v 0 k III' . f(x) g(y) (xy) "1lv (xy) dy J 0 k IV. g(y) f (x) (xy) "Kv (xy) dx J 0 k g(y) (xy) 2Y (xy)dy IV' * f(x) J v 0 V Preface...

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 cents(z) corresponding to a given q, (x) by (a) is known, then cents(z) belonging to xaq, (x) or more general...

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...