A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Generalized elliptic integrals and modular equations
Tekijät: Anderson G., Qiu S., Vamanamurthy M., Vuorinen M.
Julkaisuvuosi: 2000
Journal: Pacific Journal of Mathematics
Tietokannassa oleva lehden nimi: Pacific Journal of Mathematics
Vuosikerta: 192
Numero: 1
Aloitussivu: 1
Lopetussivu: 37
ISSN: 0030-8730
Verkko-osoite: http://api.elsevier.com/content/abstract/scopus_id:0001873330
Tiivistelmä
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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