Completely monotonic ratios of basic and ordinary gamma functions
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Completely monotonic ratios of basic and ordinary gamma functions. / Berg, Christian; Çetinkaya, Asena; Karp, Dmitrii.
In: Aequationes Mathematicae, Vol. 95, No. 3, 2021, p. 569-588.Research output: Contribution to journal › Journal article › Research › peer-review
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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