On Kaluza's sign criterion for reciprocal power series

Details On Kaluza's sign criterion for reciprocal power series On Kaluza's sign criterion for reciprocal power series

2010-10-26

arxiv.org/abs/1010.5337v3

Annales Universitatis Mariae Curie-Sklodowska. Sectio A. Mathematica 65(2) (2011) 1-16

Mathematics

Complex Variables

13 pages

Scientific paper

10.2478/v10062-011-0009-2

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\.z is applied.

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