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.
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