论文标题
$ p $ - $ q $“混合”模块化度15
$P$--$Q$ "mixed" modular equations of degree 15
论文作者
论文摘要
拉马努扬在他的第二张笔记本中记录了七个$ p $ - $ q $模块化方程，涉及theta的$ f（-q）$，带有订单1、3、5和15的模量。在本文中，与Ramanujan录制的模块化方程相似，与他的Theta-functions $ com $ umim $φ（）$ c $φ（）$ q）相似。因此，明确评估了theta功能的几个值的值和第12阶的持续比例的几个值。
Ramanujan in his second notebook recorded total of seven $P$--$Q$ modular equations involving theta--function $f(-q)$ with moduli of orders 1, 3, 5 and 15. In this paper, modular equations analogous to those recorded by Ramanujan are obtained involving his theta--functions $φ(q)$ and $ψ(-q)$ with moduli of orders 1, 3, 5 and 15. As a consequence, several values of quotients of theta--function and a continued fraction of order 12 are explicitly evaluated.
