Handbook Of Mellin Transforms

Handbook of Mellin Transforms

The Mellin transformation is widely used in various problems of pure and applied mathematics, in particular, in the theory of differential and integral equations and the theory of Dirichlet series. It is found in extensive applications in mathematical physics, number theory, mathematical statistics, theory of asymptotic expansions, and especially, in the theory of special functions and integral transformations. It is essentially used in algorithms of integration in computer algebra systems. Since the majority of integrals encountered in applications can be reduced to the form of the corresponding Mellin transforms with specific parameters, this handbook can also be used for definite and indefinite integrals. By changes in variables, the Mellin transform can be turned into the Fourier and Laplace transforms. The appendices contain formulas of connection with other integral transformations, and an algorithm for determining regions of convergence of integrals. The Handbook of Mellin Transforms will be of interest and useful to all researchers and engineers who use mathematical methods. It will become the main source of formulas of Mellin transforms, as well as indefinite and definite integrals.

Handbook of Mellin Transforms

This volume presents the tables of formulae for the evaluation of Mellin Transforms of elementary and special functions. The Handbook includes some formulae obtained by the authors and published for the first time. The tables are prefaced by a summary of notation for special functions and certain constants. The appendix contains some properties of the Mellin transform and applications. The results in tables are important for applications in different areas of mathematics, physics, mechanics, engineering, chemistry, biology and other applied sciences. The Handbook is a useful source of reference for graduate students and researchers.

Handbook of Mellin Transforms