A derivation of two quadratic transformations contiguous to that of Gauss via a differential equation approach
M Swathi, A K Rathie, R B Paris
TL;DR
This paper offers an alternative proof for two quadratic transformation formulas related to Gauss's work, using a differential equation approach to establish their validity.
Contribution
It introduces a novel differential equation method to derive quadratic transformations contiguous to Gauss's classical formulas.
Findings
Successfully derives two quadratic transformations using the differential equation approach
Provides an alternative proof to classical Gauss transformation formulas
Enhances understanding of transformation formulas through differential equations
Abstract
The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics