Communications of the
Korean Mathematical Society CKMS

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Commun. Korean Math. Soc. 2014; 29(2): 269-283

Printed April 1, 2014

https://doi.org/10.4134/CKMS.2014.29.2.269

Copyright © The Korean Mathematical Society.

Further expansion and summation formulas involving the hyperharmonic function

Sebastien Gaboury

University of Quebec at Chicoutimi

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The aim of the paper is to present several new relationships involving the hyperharmonic function introduced by Mez\"{o} in (I. Mez\"{o}, 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.

Keywords: fractional derivatives, generalized Taylor expansion, generalized Leibniz rules, integral analogue, summation formula

MSC numbers: 26A33, 33B15

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