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Integrals of Frullani type and the method of brackets

Sergio Bravo, Ivan Gonzalez, Karen Kohl, Victor H. Moll (2017)

Open Mathematics

The method of brackets is a collection of heuristic rules, some of which have being made rigorous, that provide a flexible, direct method for the evaluation of definite integrals. The present work uses this method to establish classical formulas due to Frullani which provide values of a specific family of integrals. Some generalizations are established.

On the Faraut-Koranyi hypergeometric functions in rank two

Miroslav Engliš, Genkai Zhang (2004)

Annales de l’institut Fourier

We give a complete description of the boundary behaviour of the generalized hypergeometric functions, introduced by Faraut and Koranyi, on Cartan domains of rank 2. The main tool is a new integral representation for some spherical polynomials, which may be of independent interest.

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