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The behaviour of the fourth type of Lauricella's hypergeometric series in n variables near the boundaries of its convergence region

Part of: Elementary classical functions Partial differential equations

Published online by Cambridge University Press:  09 April 2009

Megumi Saigo  and
H. M. Srivastava
Megumi Saigo
Affiliation:
Department of Applied Mathematics, Fukuoka University, Fukuoka 814-01, Japan
H. M. Srivastava
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada
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Abstract

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For Lauricella's hypergeometric function F(n)D of n variables, we prove two formulas exhibiting its behaviour near the boundaries of the n-dimensional region of convergence of the multiple series defining it. Each of these results can be applied to deduce the corresponding properties of several simpler hypergeometric functions of one, two, and more variables.

MSC classification

Secondary: 35B40: Asymptotic behavior of solutions 33C65: Appell, Horn and Lauricella functions 33B15: Gamma, beta and polygamma functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 3 , December 1994 , pp. 281 - 294
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Appell, P. and de Fériet, J. Kampé, Fonctions hypergéométriques et hypersphériques; polynômes d'Hermite (Gauthier-Villars, Paris, 1926).Google Scholar
[2]Exton, H., Multiple hypergeometric functions and applications (Halsted Press, Wiley, New York, 1976).Google Scholar
[3]Lauricella, G., ‘Sulle funzioni ipergeometriche a più variabili’, Rend. Circ. Mat. Palermo 7 (1893), 111–158.CrossRefGoogle Scholar
[4]Magnus, W., Oberhettinger, F. and Soni, R. P., Formulas and theorems for the special functions of mathematical physics (Springer, Berlin, 1966).CrossRefGoogle Scholar
[5]Saigo, M., ‘A certain boundary value problem for the Euler-Darboux equation. II and III’, Math. Japon. 25 (1980), 211–220 and 26 (1981), 103–119.Google Scholar
[6]Saigo, M., ‘On a property of the Appell hypergeometric function F 1’, Math. Rep. College General Ed. Kyushu Univ. 12 (1980), 63–67.Google Scholar
[7]Saigo, M., ‘On properties of the Appell hypergeometric functions F 2 and F 3 and the generalized Gauss function 3F 2.’, Bull. Central Res. Inst. Fukuoka Univ. 66 (1983), 27–32.Google Scholar
[8]Saigo, M., ‘On properties of hypergeometric functions of three variables, F M and FG’, Rend. Circ. Mat. Palermo (2) 37 (1988), 449–468.CrossRefGoogle Scholar
[9]Saigo, M., ‘On properties of the Lauricella hypergeometric function FD’, Bull. Central Res. Inst. Fukuoka Univ. 104 (1988), 13–31.Google Scholar
[10]Srivastava, H. M. and Daoust, M. C., ‘Certain generalized Neumann expansions associated with the Kampé de Fériet function’, Nederl. Akad. Wetensch. Indag. Math. 31 (1969), 449–457.Google Scholar
[11]Srivastava, H. M. and Karlsson, P. W., Multiple Gaussian hypergeometric series (Halsted Press, Wiley, New York, 1985).Google Scholar
[12]Srivastava, H. M. and Saigo, M., ‘Multiplication of fractional calculus operators and boundary value problems involving the Euler-Darboux equation’, J. Math. Anal. Appl. 121 (1987), 325–369.CrossRefGoogle Scholar