Generalized Elliptic Integrals and Modular Equations

G. D. Anderson, S.-L. Qiu, M. K. Vamanamurthy, and M. Vuorinen


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

Last Updated
9 April 1998

50 pages

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