| 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 $pi$. The authors study the monotoneity and convexity properties of these quantities and obtain sharp inequalities for them. |
Keywords
Zero-balanced hypergeometric functions, modular equations, signature, degree, conformal, modulus.
Math Review Classification
Primary 30C62, 33C05
; Secondary 26D15, 11F99
Last Updated
9 April 1998
Length
50 pages
Availability
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