Using Fourier-Legendre expansions to derive series for \(\frac{1}{\pi}\) and \(\frac{1}{\pi^{2}}\)
From MaRDI portal
Publication:5962078
DOI10.1007/s11139-010-9222-9zbMath1203.30005OpenAlexW2020405648MaRDI QIDQ5962078
Publication date: 16 September 2010
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11139-010-9222-9
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) General harmonic expansions, frames (42C15) Calculation of integer sequences (11Y55)
Related Items (17)
From Wallis and Forsyth to Ramanujan ⋮ On a \(q\)-deformation of modular forms ⋮ Further WZ-based methods for proving and generalizing Ramanujan's series ⋮ GAUSS SUMMATION AND RAMANUJAN-TYPE SERIES FOR 1/π ⋮ Binomial identities obtained from the Gegenbauer series expansion ⋮ \(\pi \)-formulas implied by Dougall's summation theorem for \(_{5} F _{4}\)-series ⋮ On a higher-order version of a formula due to Ramanujan ⋮ Applications of a hypergeometric identity and Ramanujan-like series ⋮ Extensions of Ramanujan's two formulas for \(1/\pi\) ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums ⋮ Hypergeometry of the Parbelos ⋮ Extensions of the classical theorems for very well-poised hypergeometric functions ⋮ A summation formula and Ramanujan type series ⋮ On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions ⋮ Accelerating Dougall’s $_5F_4$-sum and infinite series involving $\pi $
Cites Work
This page was built for publication: Using Fourier-Legendre expansions to derive series for \(\frac{1}{\pi}\) and \(\frac{1}{\pi^{2}}\)
