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Displaying similar documents to “Series and iterations for 1/π”

A continued fraction of order twelve

M. Mahadeva Naika, B. Dharmendra, K. Shivashankara (2008)

Open Mathematics

Similarity:

In this paper, we establish several explicit evaluations, reciprocity theorems and integral representations for a continued fraction of order twelve which are analogues to Rogers-Ramanujan’s continued fraction and Ramanujan’s cubic continued fraction.

Modular equations for some η-products

(2013)

Acta Arithmetica

Similarity:

The classical modular equations involve bivariate polynomials that can be seen to be univariate in the modular invariant j with integer coefficients. Kiepert found modular equations relating some η-quotients and the Weber functions γ₂ and γ₃. In the present work, we extend this idea to double η-quotients and characterize all the parameters leading to this kind of equation. We give some properties of these equations, explain how to compute them and give numerical examples.