2015/07/23 by Giovanni Mingari Scarpello, Scarpello, Giovanni Mingari, Daniele Ritelli +1
Computer Science · Mathematics · Physics and Astronomy · #11Y60 #33C65 #33C75 #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1507.06681
openalex publication_date 2015/07/23 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
In this article we developed a special topic of our pure-mathematics papers concerning the hypergeometric theory. Based upon a Roberts's reduction approach of hyperelliptic integrals to elliptic ones and on the simultaneous multivariable hypergeometric series evaluation of them, several identities have been obtained expressing π in terms of special values of elliptic, hypergeometric and Gamma functions. By them π can be provided through either only one or two parameters and through the imaginary unit. In any case, such results, all unpublished and undoubtably new, will provide, beyond their own beauty, a useful tool in order to check the routines (more or less naive) which one can build for the practical computations of Lauricella's functions met frequently in researches on Mechanics or Elasticity.