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Further expansion and summation formulas involving the hyperharmonic function

Sebastien Gaboury
대한수학회 (The Korean Mathematical Society)|2014.04|대한수학회논문집 (Communications of the KMS)|제29권 제2호|pp. 269-283

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참고문헌

키워드

fractional derivativesgeneralized Taylor expansiongeneralized Leibniz rulesintegral analoguesummation formula
주제분류수학

초록

The aim of the paper is to present several new relationships involving the hyperharmonic function introduced by Mezö in (I. Mezö, Analytic extension of hyperharmonic numbers, Online J. Anal. Comb. 4, 2009) which is an analytic extension of the hyperharmonic numbers. These relations are obtained by using some fractional calculus theorems as Leibniz rules and Taylor like series expansions.

Abstract

The aim of the paper is to present several new relationships involving the hyperharmonic function introduced by Mezö in (I. Mezö, Analytic extension of hyperharmonic numbers, Online J. Anal. Comb. 4, 2009) which is an analytic extension of the hyperharmonic numbers. These relations are obtained by using some fractional calculus theorems as Leibniz rules and Taylor like series expansions.

참고문헌 (27)

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