Series Transformation Formulas of Euler Type, Hadamard Product of Functions, and Harmonic Number Identities
arXiv:0912.5376
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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- Convolutions for Stirling numbers, Lah numbers, and binomial coefficients
- Power series with inverse binomial coefficients and harmonic numbers
- Evaluation of binomial series with harmonic numbers
- Series with Hermite Polynomials and Harmonic Numbers