Series Transformation Formulas of Euler Type, Hadamard Product of Functions, and Harmonic Number Identities
Abstract
The integral representation of the Hadamard product of two functions is used to prove several Euler-type series transformation formulas. As applications we obtain three 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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