Moments of products of elliptic integrals

Moments of products of elliptic integrals

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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Veröffentlicht in:Advances in applied mathematics 2012, Vol.48 (1), p.121-141
1. Verfasser: Wan, James G.
Format: Artikel
Sprache:eng
Schlagworte:
Elliptic integrals
Experimentation
Generalised hypergeometric series
Mathematical models
Moments
Theorems
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Beschreibung
Zusammenfassung: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.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2011.04.007