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On some conjectures of Askey

Article type: Research Article

Authors: Volkmer, Hans

Affiliations: Department of Mathematical Sciences, University of Wisconsin‐Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA Tel.: (414) 229‐5950, Fax: (414) 229‐4907, E‐mail: volkmer@uwm.edu

Abstract: Using the Darboux method of asymptotic analysis, it is shown that the coefficients of the power series expansions of the functions f(w)=(1−w)−c(1−2xw+w2)−c and (1+w)f(w), 1<c<2, at w=0 are positive if x lies in certain intervals. This partially answers some questions raised by Askey.

Journal: Asymptotic Analysis, vol. 27, no. 3-4, pp. 321-334, 2001

Published: 2001
Price: EUR 27.50
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