Summation formulas involving binomial coefficients, harmonic numbers, and generalized harmonic numbers
type: Item
instance of: scholarly article
title: Summation formulas involving binomial coefficients, harmonic numbers, and generalized harmonic numbers
zbMATH Open document ID: 1422.11033
DOI: 10.1155/2014/501906
author: Junesang Choi
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics, and theoretical physics. Here we show how one can obtain further interesting and (almost) serendipitous identities about certain finite or infinite series involving binomial coefficients, harmonic numbers, and generalized harmonic numbers by simply applying the usual differential operator to well-known Gauss's summation formula for \(_2F_1(1)\).
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 7022498
Wikidata QID: Q59038834
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/501906
OpenAlex ID: W2148072272
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description: scientific article; zbMATH DE number 7022498