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On the location of the singularities of the function generated by the Bergman operator of the second kind


Author: Paul Rosenthal
Journal: Proc. Amer. Math. Soc. 44 (1974), 157-162
MSC: Primary 35C15
DOI: https://doi.org/10.1090/S0002-9939-1974-0328293-4
MathSciNet review: 0328293
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Abstract: Let $ g(x,y) = {P_2}(f)$ be Bergman's operator of the second kind, $ f(q)$ analytic at $ q = 0$. The purpose of this paper is to generalize a previous result of the author on the location of the singularities of $ g(x,y)$ when $ f(q)$ had only a simple pole. $ f(q)$ now is assumed to be a rational function whose poles are distributed along the arc of a circle. An order relation is also obtained for $ g(x,y)$ for certain fixed $ x$ and $ y$ sufficiently large and positive.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0328293-4
Keywords: Bergman operator of the second kind, hypergeometric function, singular points
Article copyright: © Copyright 1974 American Mathematical Society