Abstract
We extend some results of Euler related sums. Integral and closed-form representations of sums with products of harmonic numbers and binomial coefficients are developed in terms of Polygamma functions. The various representations presented in this paper are believed to be new.
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Sofo, A., Srivastava, H.M. Identities for the harmonic numbers and binomial coefficients. Ramanujan J 25, 93–113 (2011). https://doi.org/10.1007/s11139-010-9228-3
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DOI: https://doi.org/10.1007/s11139-010-9228-3
Keywords
- Harmonic numbers
- Riemann zeta function
- Polylogarithms
- Integral representations
- Binomial coefficients
- Euler sums
- Digamma functions
- Polygamma functions
- Catalan’s constant
- Bernoulli polynomials
- Clausen function