2022/10/30 by Omran Kouba, Kouba, Omran
Mathematics · #33C20 #33C45 #42C10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.2210.16784
openalex publication_date 2022/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the expansion in a Fourier-Gegenbauer series, we prove several identities that extend and generalize known results. In particular, it is proved among other results, that ∑n=0^∞(1)/(4n)\binom2nn\fracz-2n\binomz-1/2n\binomzn3 =\fractan(πz)π for all complex numbers z such that \Re(z)>-(1)/(2) and z∉(1)/(2)+ℤ.