On some modular equations of degree $5$
Author: Li-Chien Shen
Journal: Proc. Amer. Math. Soc. 123 (1995), 1521-1526
MSC: Primary 33D10; Secondary 11B65
MathSciNet review: 1273524
Full-text PDF Free Access
Abstract: The main purpose of this paper is to examine certain well-known modular equations of degree 5 from a very intuitive angle. Unlike the classical treatment of this subject, which requires parametrization of certain key quantities, we will give direct proofs to these equations by recasting them as theta function identities which are quite interesting in their own right.
B. C. Berndt, Ramanujan’s notebooks, part III, Springer-Verlag, New York, 1991.
E. T. Whittaker and G. N. Watson, Modern analysis, 4th edition, Cambridge Univ. Press, 1958.