Completely monotonic ratios of basic and ordinary gamma functions

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Standard

Completely monotonic ratios of basic and ordinary gamma functions. / Berg, Christian; Çetinkaya, Asena; Karp, Dmitrii.

I: Aequationes Mathematicae, Bind 95, Nr. 3, 2021, s. 569-588.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Berg, C, Çetinkaya, A & Karp, D 2021, 'Completely monotonic ratios of basic and ordinary gamma functions', Aequationes Mathematicae, bind 95, nr. 3, s. 569-588. https://doi.org/10.1007/s00010-020-00767-6

APA

Berg, C., Çetinkaya, A., & Karp, D. (2021). Completely monotonic ratios of basic and ordinary gamma functions. Aequationes Mathematicae, 95(3), 569-588. https://doi.org/10.1007/s00010-020-00767-6

Vancouver

Berg C, Çetinkaya A, Karp D. Completely monotonic ratios of basic and ordinary gamma functions. Aequationes Mathematicae. 2021;95(3):569-588. https://doi.org/10.1007/s00010-020-00767-6

Author

Berg, Christian ; Çetinkaya, Asena ; Karp, Dmitrii. / Completely monotonic ratios of basic and ordinary gamma functions. I: Aequationes Mathematicae. 2021 ; Bind 95, Nr. 3. s. 569-588.

Bibtex

@article{3821b2c219ee4a6f9f294d3081e56c24,
title = "Completely monotonic ratios of basic and ordinary gamma functions",
abstract = "We investigate conditions for logarithmic complete monotonicity of product ratios of gamma and q-gamma functions whose arguments are linear functions of the variable. We give necessary and sufficient conditions in terms of nonnegativity of a certain explicitly written measure in the q case and of a certain elementary function in the classical q= 1 case. In the latter case we further provide simple new sufficient conditions leading to many new examples of logarithmically completely monotonic gamma ratios. Finally, we apply some of our results to study monotonicity of some gamma ratios and rational functions.",
keywords = "Bernstein function, Completely monotonic function, Digamma function, Gamma function, Logarithmic complete monotonicity, q-Gamma function, Sherman{\textquoteright}s theorem",
author = "Christian Berg and Asena {\c C}etinkaya and Dmitrii Karp",
note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.",
year = "2021",
doi = "10.1007/s00010-020-00767-6",
language = "English",
volume = "95",
pages = "569--588",
journal = "Aequationes Mathematicae",
issn = "0001-9054",
publisher = "Springer Basel AG",
number = "3",

}

RIS

TY - JOUR

T1 - Completely monotonic ratios of basic and ordinary gamma functions

AU - Berg, Christian

AU - Çetinkaya, Asena

AU - Karp, Dmitrii

N1 - Publisher Copyright: © 2021, Springer Nature Switzerland AG.

PY - 2021

Y1 - 2021

N2 - We investigate conditions for logarithmic complete monotonicity of product ratios of gamma and q-gamma functions whose arguments are linear functions of the variable. We give necessary and sufficient conditions in terms of nonnegativity of a certain explicitly written measure in the q case and of a certain elementary function in the classical q= 1 case. In the latter case we further provide simple new sufficient conditions leading to many new examples of logarithmically completely monotonic gamma ratios. Finally, we apply some of our results to study monotonicity of some gamma ratios and rational functions.

AB - We investigate conditions for logarithmic complete monotonicity of product ratios of gamma and q-gamma functions whose arguments are linear functions of the variable. We give necessary and sufficient conditions in terms of nonnegativity of a certain explicitly written measure in the q case and of a certain elementary function in the classical q= 1 case. In the latter case we further provide simple new sufficient conditions leading to many new examples of logarithmically completely monotonic gamma ratios. Finally, we apply some of our results to study monotonicity of some gamma ratios and rational functions.

KW - Bernstein function

KW - Completely monotonic function

KW - Digamma function

KW - Gamma function

KW - Logarithmic complete monotonicity

KW - q-Gamma function

KW - Sherman’s theorem

U2 - 10.1007/s00010-020-00767-6

DO - 10.1007/s00010-020-00767-6

M3 - Journal article

AN - SCOPUS:85098496618

VL - 95

SP - 569

EP - 588

JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

SN - 0001-9054

IS - 3

ER -

ID: 306972211