|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.
Zero-balanced hypergeometric functions, modular equations, signature, degree, conformal, modulus.
Math Review Classification
Primary 30C62, 33C05 ; Secondary 26D15, 11F99
9 April 1998
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