Harmonic numbers and double binomial coefficients
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Publication:3651167
DOI10.1080/10652460902917844zbMath1242.11014OpenAlexW2135651265MaRDI QIDQ3651167
Publication date: 8 December 2009
Published in: Integral Transforms and Special Functions (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/10652460902917844
combinatorial identitieshypergeometric functionsintegral representationsbinomial coefficientsharmonic numbers
Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65) Generalized hypergeometric series, ({}_pF_q) (33C20)
Related Items (17)
Parametric binomial sums involving harmonic numbers ⋮ Identities for Reciprocal Binomials ⋮ Euler sums and Stirling sums ⋮ Infinite series around multinomial coefficients and harmonic numbers ⋮ Sums of quadratic half integer harmonic numbers of alternating type ⋮ Half-integer values of the sums of harmonic numbers of order two ⋮ Harmonic numbers and cubed binomial coefficients ⋮ New families of alternating harmonic number sums ⋮ Harmonic number identities via the Newton-Andrews method ⋮ Identities for the harmonic numbers and binomial coefficients ⋮ Summation formula involving harmonic numbers ⋮ Harmonic numbers at half integer values ⋮ Minton-Karlsson identities and summation formulae involving generalized harmonic numbers ⋮ Integrals of polylogarithmic functions with alternating argument ⋮ On certain series involving reciprocals of binomial coefficients ⋮ Harmonic sums and integral representations ⋮ A family of summation formulae involving harmonic numbers
Cites Work
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- On the series \(\sum_{k=1}^\infty \binom {3k}{k}^{-1} k^{-n}x^k\)
- Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent
- Integral forms of sums associated with harmonic numbers
- Automatic generation of hypergeometric identities by the beta integral method.
- Series representations for some mathematical constants
- Some combinatorial series identities and rational sums
- Some more identities involving rational sums
- Double Integrals for Euler's Constant and in $\frac{4}{\pi}$ and an Analog of Hadjicostas's Formula
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