Further expansion and summation formulas involving the hyperharmonic function
Commun. Korean Math. Soc. 2014 Vol. 29, No. 2, 269-283
https://doi.org/10.4134/CKMS.2014.29.2.269
Printed April 1, 2014
Sebastien Gaboury
University of Quebec at Chicoutimi
Abstract : 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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