☆ 4.2 Article

INFINITE SERIES CONCERNING HARMONIC NUMBERS AND QUINTIC CENTRAL BINOMIAL COEFFICIENTS

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY (2023)

Infinite series identities derived from the very well-poised Ω-sum

Wenchang Chu

Summary: The well-poised Omega-series has a universal iteration pattern, which can generate numerous infinite series identities, including several important ones discovered by Ramanujan in 1914 and recently by Guillera.

RAMANUJAN JOURNAL (2021)

添加到收藏夹

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)

添加到收藏夹

Article Mathematics

Further Apery-Like Series for Riemann Zeta Function

Wenchang Chu

Summary: Using two transformation formulas of classical hypergeometric series, several Apery-like series for the Riemann zeta function involving higher order harmonic numbers are derived, including some identities conjectured by Sun (2015).

MATHEMATICAL NOTES (2021)

添加到收藏夹

Article Mathematics