Lemniscate-like constants and infinite series

DOI10.1515/ms-2021-0025zbMath1492.33001OpenAlexW3189746013MaRDI QIDQ2054730

John Maxwell Campbell, Chu, Wenchang

Publication date: 3 December 2021

Published in: Mathematica Slovaca (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ms-2021-0025

zbMATH Keywords

harmonic seriesbinomial coefficientbeta integrallemniscate constantKummer's theoremGauss' lemniscate sine function

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Other functions defined by series and integrals (33E20) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (5)

A note on Clebsch-Gordan integral, Fourier-Legendre expansions and closed form for hypergeometric series ⋮ A series evaluation technique based on a modified Abel lemma ⋮ On a higher-order version of a formula due to Ramanujan ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

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• Sharp Shafer-Fink type inequalities for Gauss lemniscate functions
• Inequalities for Jacobian elliptic functions and Gauss lemniscate functions
• The lemniscate and Fagnano's contributions to elliptic integrals
• Logarithmically complete monotonicity properties relating to the gamma function
• Ramanujan-like series for \(\frac{1}{\pi}\) involving harmonic numbers
• Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients
• New properties of the lemniscate function and its transformation
• Ramanujan's inversion formulas for the lemniscate and allied functions
• On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums
• Harmonic sums from the Kummer theorem
• New series involving harmonic numbers and squared central binomial coefficients
• Padé approximant related to inequalities for Gauss lemniscate functions
• On rational bounds for the gamma function
• Series containing squared central binomial coefficients and alternating harmonic numbers
• 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
• The lemniscate constants
• On lemniscate functions
• Symbolic computations via Fourier–Legendre expansions and fractional operators
• Sharp rational bounds for the gamma function

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