On Kaluza's sign criterion for reciprocal power series

Árpád Baricz; Jetro Vesti; Matti Vuorinen

Annales UMCS, Mathematica (2011)

  • Volume: 65, Issue: 2, page 1-16
  • ISSN: 2083-7402

Abstract

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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.

How to cite

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Árpád Baricz, Jetro Vesti, and Matti Vuorinen. "On Kaluza's sign criterion for reciprocal power series." Annales UMCS, Mathematica 65.2 (2011): 1-16. <http://eudml.org/doc/267915>.

@article{ÁrpádBaricz2011,
abstract = {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.},
author = {Árpád Baricz, Jetro Vesti, Matti Vuorinen},
journal = {Annales UMCS, Mathematica},
keywords = {Power series; log-convexity; hypergeometric functions; trigonometric functions},
language = {eng},
number = {2},
pages = {1-16},
title = {On Kaluza's sign criterion for reciprocal power series},
url = {http://eudml.org/doc/267915},
volume = {65},
year = {2011},
}

TY - JOUR
AU - Árpád Baricz
AU - Jetro Vesti
AU - Matti Vuorinen
TI - On Kaluza's sign criterion for reciprocal power series
JO - Annales UMCS, Mathematica
PY - 2011
VL - 65
IS - 2
SP - 1
EP - 16
AB - 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.
LA - eng
KW - Power series; log-convexity; hypergeometric functions; trigonometric functions
UR - http://eudml.org/doc/267915
ER -

References

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