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The Ramanujan Journal

, Volume 25, Issue 3, pp 369–387 | Cite as

A transformation of certain infinite series based on the non-local derangement identity

  • Marian Genčev
Article

Abstract

The aim of the paper is a new transformation of certain infinite series based on an identity from Sylvester also known as the non-local derangement identity. Surprisingly, the result found can be applied to evaluate certain types of the generalized hypergeometric function p F q (z) or infinite series involving the combination of hyperbolic functions, irrational functions and polynomials like some of which seem to be new. On the other hand, for those which are known, our approach provides a new method to derive the discussed identities using a simple algorithm.

Keywords

Infinite series Transformations Summation theorems Hypergeometric function 

Mathematics Subject Classification (2000)

40A25 40G99 33C20 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Faculty of EconomicsVŠB—Technical UniversityOstravaCzech Republic

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