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2001/2002 Monotonicity of Coefficients of Reciprocal Power Series
Eduardo H. M. Brietzke
Real Anal. Exchange 27(1): 41-48 (2001/2002).


Given a power series $f(x)=\sum_{n=1}^\infty\,a_n\,x^n$ with nonnegative coefficients satisfying $\sum_{n=1}^\infty\,a_n=1$ we give sufficient conditions on the sequence $(a_n)$ to guarantee that the coefficients of the Taylor series of $h(x)=1/(1-f(x))$ form a nonincreasing sequence. This type of result is useful when one wishes to apply Tauberian theorems.


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Eduardo H. M. Brietzke. "Monotonicity of Coefficients of Reciprocal Power Series." Real Anal. Exchange 27 (1) 41 - 48, 2001/2002.


Published: 2001/2002
First available in Project Euclid: 6 June 2008

zbMATH: 1021.30005
MathSciNet: MR1887680

Primary: 30B10 , ‎39B62 , 65Q05

Keywords: Monotonicity of Coefficients , renewal equation , Tauberian theorems

Rights: Copyright © 2001 Michigan State University Press

Vol.27 • No. 1 • 2001/2002
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