Moments of Ramanujan’s Generalized Elliptic Integrals and Extensions of Catalan’s Constant
نویسنده
چکیده
We undertake a thorough investigation of the moments of Ramanujan’s alternative elliptic integrals and of related hypergeometric functions. Along the way we are able to give some surprising closed forms for Catalan-related constants and various new hypergeometric identities.
منابع مشابه
Generalized Elliptic Integrals and Modular Equations
In geometric function theory, generalized elliptic integrals and functions arise from the Schwarz-Christoffel transformation of the upper half-plane onto a parallelogram and are naturally related to Gaussian hypergeometric functions. Certain combinations of these integrals also occur in analytic number theory in the study of Ramanujan’s modular equations and approximations to π. The authors stu...
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