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.
@article{bwmeta1.element.doi-10_2478_v10062-011-0009-2,
author = {\'Arp\'ad Baricz and Jetro Vesti and Matti Vuorinen},
title = {On Kaluza's sign criterion for reciprocal power series},
journal = {Annales UMCS, Mathematica},
volume = {65},
year = {2011},
pages = {1-16},
zbl = {1260.30002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-011-0009-2}
}
Árpád Baricz; Jetro Vesti; Matti Vuorinen. On Kaluza's sign criterion for reciprocal power series. Annales UMCS, Mathematica, Tome 65 (2011) pp. 1-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-011-0009-2/
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