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Series transformation formulas of Euler type, Hadamard product of series, and harmonic number identities

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Abstract

The Hadamard multiplication theorem for series is used to establish several Euler-type series transformation formulas. As applications we obtain a number of binomial identities involving harmonic numbers and an identity for the Laguerre polynomials. We also evaluate in a closed form certain power series with harmonic numbers.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Ohio Northern University, Ada, Ohio, 45810, USA

    Khristo N. Boyadzhiev

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  1. Khristo N. Boyadzhiev
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Correspondence to Khristo N. Boyadzhiev.

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Boyadzhiev, K.N. Series transformation formulas of Euler type, Hadamard product of series, and harmonic number identities. Indian J Pure Appl Math 42, 371–386 (2011). https://doi.org/10.1007/s13226-011-0024-6

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  • DOI: https://doi.org/10.1007/s13226-011-0024-6

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