Moments of Products of Elliptic Integrals
James Wan
TL;DR
This paper investigates the moments of products of elliptic integrals, deriving new results through elementary methods, computer experimentation, and a theorem, while also presenting related evaluations and conjectures.
Contribution
It introduces new explicit formulas for moments of elliptic integral products using elementary techniques and computational tools, expanding existing knowledge.
Findings
New formulas for moments of elliptic integral products
Diverse related evaluations provided
Two conjectures proposed
Abstract
We consider the moments of products of complete elliptic integrals of the first and second kinds. In particular, we derive new results using elementary means, aided by computer experimentation and a theorem of W. Zudilin. Diverse related evaluations, and two conjectures, are also given.
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Taxonomy
TopicsMathematical functions and polynomials · Mathematical Inequalities and Applications · Analytic Number Theory Research