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Infinite series on quadratic skew harmonic numbers

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS (2023)

Harmonic-binomial Euler-like sums via expansions of (arcsin x)p

Amrik Singh Nimbran et al.

Summary: In this paper, we evaluate a class of Euler-like sums involving harmonic/odd harmonic numbers and central binomial coefficients using the expansion for powers of the inverse sine function. We also evaluate several integrals that lead to new identities for central binomial coefficients and harmonic numbers.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS (2022)

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Article Mathematics, Applied

A Wilf-Zeilberger-based solution to the Basel problem with applications

John M. Campbell

Summary: In this article, a remarkable identity for a F-3(2) (1)-series that cannot be directly evaluated by Maple 2020 is proved using the WZ method. The WZ proof of this identity is then applied to obtain a new proof of the famous formula zeta(2) = pi(2)/6. Additionally, by applying partial derivative operators, several open problems involving series with harmonic-type numbers and squared binomial coefficients are solved.

DISCRETE MATHEMATICS LETTERS (2022)

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Article Mathematics, Applied

Harmonic sums from the Kummer theorem

Wenchang Chu et al.

Summary: The Kummer summation theorem for F-2(1)(-1)-series is extended with three integer parameters and examined by power series expansions, leading to various new alternating series involving harmonic-like numbers and squared central binomial coefficients. Coefficient extraction methods are used to obtain closed form evaluations for these series, and new identities for integrals involving complete elliptic integrals with complex arguments are also derived using the same approach.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2021)

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Article Mathematics