%0 Journal Article
%T On Kaluza's sign criterion for reciprocal power series
%A ¨¢rp¨¢d Baricz
%A Jetro Vesti
%A Matti Vuorinen
%J Annales UMCS, Mathematica
%D 2011
%I 
%R 10.2478/v10062-011-0009-2
%X T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzy  is applied.
%K Power series
%K log-convexity
%K hypergeometric functions
%K trigonometric functions
%U http://versita.metapress.com/content/t513l2400276u556/?p=9e685f8f8e3c43feac8c2f72770a2544&pi=1