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On Kaluza's sign criterion for reciprocal power series

Árpád BariczJetro VestiMatti Vuorinen — 2011

Annales UMCS, Mathematica

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.

On Kaluza’s sign criterion for reciprocal power series

Arpad BariczJetro VestiMatti Vuorinen — 2011

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

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.

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