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The Common Limit of a Quadruple Sequence and the Hypergeometric Function Fd of Three Variables

Published online by Cambridge University Press:  11 January 2016

Takayuki Kato  and
Keiji Matsumoto
Takayuki Kato
Affiliation:
MEC INC., 2-6 Futuka, Aoba-ku Sendai 980-0802, Japankatou-t@mec-inc.co.jp
Keiji Matsumoto
Affiliation:
Department of MathematicsHokkaido University, Sapporo 060-0810, Japanmatsu@math.sci.hokudai.ac.jp
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Abstract

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We study a quadruple sequence and express its common limit by Lauricella’s hypergeometric function FD(¼,¼,¼.¼, 1; z1, z2, z3)of three variables. We give a functional equation of FD, which is the key to get our expression of the common limit.

Keywords

26A1833C65
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 195 , 2009 , pp. 113 - 124
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

References

[B] Borchardt, C. W., über das arithmetisch-geometrische Mittel aus vier Elementen,Berl. Monatsber, 53 (1876), 611–621.Google Scholar
[BB] Borwein, J. M. and Borwein, P. B., A cubic counterpart of Jacobi’s identity and the AGM, Trans. Amer. Math. Soc., 323 (2) (1991), 691–701.Google Scholar
[IKSY] Iwasaki, K., Kimura, H., Shimomura, S. and Yoshida, M., From Gauss to Painlevé, Vieweg, Braunschweig, Wiesbaden, 1991.CrossRefGoogle Scholar
[KS1] Koike, K. and Shiga, H., Isogeny formulas for the Picard modular form and a three terms arithmetic geometric mean, J. Number Theory, 124 (2007), 123–141.CrossRefGoogle Scholar
[KS2] Koike, K. and Shiga, H., Extended Gauss AGM and corresponding Picard modular forms, J. Number Theory, 128 (2008), 2097–2126.CrossRefGoogle Scholar
[M] Mestre, J. F., Moyenne de Borchardt et intégrales elliptiques, Acad. Sci. Paris, 313 (1991), 273–276.Google Scholar
[MM] Manna, D. V. and Moll, V. H., Landen survey, Probability, Geometry and Integrable Systems, MSRI Publications, 55, Cambridge University Press, Cambridge, 2008, pp. 287–319.Google Scholar
[O] Ohara, K., yang — a package for computation in the ring of differential-difference operators, http://www.openxm.org, 2007.Google Scholar