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An extension of the method of brackets. Part 1

100%

Gonzalez I., Kohl K., Jiu L., Moll V. H.

Open Mathematics

2017

tom 15

nr 1

1181-1211

The method of brackets is an efficient method for the evaluation of alarge class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the concepts of null and divergent series. These are formal representations of functions, whose coefficients an have meromorphic representations for n ∈ ℂ, but might vanish or blow up when n ∈ ℕ. These ideas are illustrated with the evaluation of a variety of entries from the classical table of integrals by Gradshteyn and Ryzhik.

Integrals of Frullani type and the method of brackets

100%

Bravo S., Gonzalez I., Kohl K., Moll V. H.

Open Mathematics

2017

tom 15

nr 1

1-12

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.

Ograniczanie wyników

2 Open Mathematics

2 Gonzalez I.

2 Kohl K.

2 Moll V. H.

1 Bravo S.

1 Jiu L.

2 2017

Wyniki wyszukiwania

An extension of the method of brackets. Part 1

Integrals of Frullani type and the method of brackets