An extension of the method of brackets. Part 1

• Autorzy: Ivan Gonzalez , Karen Kohl , Lin Jiu , Victor H. Moll
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Definite integrals; Method of brackets; Divergent series

Kategorie tematyczne

• 33F10: Symbolic computation (Gosper and Zeilberger algorithms, etc.)
• 33C05: Classical hypergeometric functions, 2 F 1

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 1181-1211

Daty

wydano

2017-01-01

otrzymano

2017-04-01

zaakceptowano

2017-08-16

online

2017-09-27

Twórcy

autor

Ivan Gonzalez

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autor

Karen Kohl

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autor

Lin Jiu

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autor

Victor H. Moll

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Identyfikatory

DOI

10.1515/math-2017-0100