Geodesic
On Kaluza’s sign criterion for reciprocal power series
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 65 (2011) no. 2.

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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. Krzyż is applied.
Keywords: Power series, log-convexity, hypergeometric functions, trigonometric functions 
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Baricz, Arpad; Vesti, Jetro; Vuorinen, Matti. On Kaluza’s sign criterion for reciprocal power series. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 65 (2011) no. 2. http://geodesic.mathdoc.fr/item/AUM_2011_65_2_a12/

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