RT Journal Article
T1 Uniform asymptotic estimates of hypergeometric functions appearing in Potential Theory
A1 Pestana, Domingo
A1 Rodríguez, José M.
AB The solution of a Dirichlet problem for the Laplace-Beltrami operator with Bergman metric in the unit ball in the complex $n$-dimensional space can be expressed in terms of integrals of which the kernel can be expanded in spherical harmonics. The coefficients in this expansion contain ratios of Gauss hypergeometric functions of the form $F(p,q;p+q+n;r^2)/ F(p,q;p+q+n;1)$. The paper studies the uniform asymptotic behaviour of $F(q,mq;q+mq+n;t)$ for large values of $q$. Several results are formulated as inequalities for certain integrals containing ratios of hypergeometric functions [Zentralblatt MATH].
PB International Press
SN 1073-2772
YR 1996
FD 1996-03
LK https://hdl.handle.net/10016/6504
UL https://hdl.handle.net/10016/6504
LA eng
NO 19 pages, no figures.-- MSC1991 codes: 33C05, 33C55, 31B15.
NO MR#: MR1393128 (98b:33007)
NO Zbl#: Zbl 0864.33001
NO Research of the second author was supported by a grant of the CICYT, Ministerio de Educación y Ciencia, Spain.
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RD 20 may. 2024