The First Derivative of Ramanujans Cubic Continued Fraction

TL;DR

This paper provides a comprehensive evaluation of the first derivative of Ramanujan's cubic continued fraction using elliptic functions, expressing results in terms of Gamma functions and radicals for easier computation.

Contribution

It offers the first complete evaluation of the derivative of Ramanujan's cubic continued fraction with explicit formulas involving elliptic functions, Gamma functions, and radicals.

Findings

Explicit formulas for the derivative in terms of elliptic functions.

Results expressed using Gamma functions and radicals.

Simplifies the evaluation process for Ramanujan's cubic continued fraction derivative.

Abstract

We give the complete evaluation of the first derivative of the Ramanujans cubic continued fraction using Elliptic functions. The Elliptic functions are easy to handle and give the results in terms of Gamma functions and radicals from tables.