Harmonic sums from the Kummer theorem
From MaRDI portal
Publication:2033210
DOI10.1016/j.jmaa.2021.125179zbMath1471.33003OpenAlexW3142790969MaRDI QIDQ2033210
John Maxwell Campbell, Chu, Wenchang
Publication date: 14 June 2021
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2021.125179
hypergeometric seriesharmonic numbersymbolic evaluationcentral binomial coefficientKummer summation theorem\(\Gamma\)-function
Binomial coefficients; factorials; (q)-identities (11B65) Gamma, beta and polygamma functions (33B15) Classical hypergeometric functions, ({}_2F_1) (33C05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)
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Cites Work
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- Ramanujan-like series for \(\frac{1}{\pi}\) involving harmonic numbers
- Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients
- Hypergeometric approach to Weideman's conjecture
- Hypergeometric series and harmonic number identities
- On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums
- A method for proving Ramanujan's series for \(1/\pi\)
- New series involving harmonic numbers and squared central binomial coefficients
- On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions
- Series containing squared central binomial coefficients and alternating harmonic numbers
- Hypergeometric identities for 10 extended Ramanujan-type series
- Harmonic number identities via hypergeometric series and Bell polynomials
- Dougall’s bilateral ₂𝐻₂-series and Ramanujan-like 𝜋-formulae
- Analytical formulae for extended $_{3}F_{2}$-series of Watson–Whipple–Dixon with two extra integer parameters
- Terminating ₂𝐹₁(4)-series perturbed by two integer parameters
- Definite integrals of the complete elliptic integral K
- Hypergeometric series and the Riemann zeta function
- Generalized harmonic number summation formulae via hypergeometric series and digamma functions
- On derivatives of hypergeometric functions and classical polynomials with respect to parameters
- Hypergeometric approach to Apéry-like series
- An integral transform related to series involving alternating harmonic numbers
- Multiple Elliptic Integrals
