A1 Refereed original research article in a scientific journal
Generalized elliptic integrals and modular equations
Authors: Anderson G., Qiu S., Vamanamurthy M., Vuorinen M.
Publication year: 2000
Journal: Pacific Journal of Mathematics
Journal name in source: Pacific Journal of Mathematics
Volume: 192
Issue: 1
First page : 1
Last page: 37
ISSN: 0030-8730
Web address : http://api.elsevier.com/content/abstract/scopus_id:0001873330
Abstract
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 study the monotoneity and convexity properties of these quantities and obtain sharp inequalities for them.
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 study the monotoneity and convexity properties of these quantities and obtain sharp inequalities for them.
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