Legendre hyperelliptic integrals, π new formulae and Lauricella functions through the elliptic singular moduli

Mingari Scarpello, Giovanni ; Ritelli, Daniele (2014) Legendre hyperelliptic integrals, π new formulae and Lauricella functions through the elliptic singular moduli. Journal of Number Theory, 135 . pp. 334-352. ISSN 0022-314X
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Abstract

This paper, pursuing the work started by tha authots, holds six new formulae for π through ratios of first kind complete elliptic integrals and some values of hypergeometric functions of three or four variables of Lauricella type. This will be accomplished by reducing some hyperelliptic integrals to elliptic through the methods Legendre taught in his treatise. The complete elliptic integrals of first kind have complementary moduli: as a consequence we can find their ratio through the Lauricella functions. In such a way we succeed in obtaining, through the theory of elliptic singular moduli, some particular values of Lauricella's themselves.

Abstract
Document type
Article
Creators
CreatorsAffiliationORCID
Mingari Scarpello, Giovanni
Ritelli, Daniele
Keywords
Reduction of Hyperelliptic Integrals; Complete Elliptic Integral of first kind; π; Hypergeometric Functions; Lauricella Function; Elliptic Singular Moduli.
Subjects
ISSN
0022-314X
DOI
Deposit date
18 Nov 2013 10:23
Last modified
10 Feb 2014 10:38
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