Series Transformation Formulas of Euler Type, Hadamard Product of Functions, and Harmonic Number Identities

Details Series Transformation Formulas of Euler Type, Hadamard Product of Functions, and Harmonic Number Identities Series Transformation Formulas of Euler Type, Hadamard Product of Functions, and Harmonic Number Identities

2009-12-29

arxiv.org/abs/0912.5376v1

Mathematics

Number Theory

Scientific paper

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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