In this paper, we introduce some monotonicity rules for the ratio of integrals. Furthermore, we demonstrate that the function is completely monotonic in and absolutely monotonic in if and only if , where defined on and is the modified Bessel function of the second kind of order . Finally, we determine the necessary and sufficient conditions for the functions , , and to be monotonic in by employing the monotonicity rules.
Accepté le :
Publié le :
Zhong-Xuan Mao 1 ; Jing-Feng Tian 2
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@article{CRMATH_2023__361_G1_217_0, author = {Zhong-Xuan Mao and Jing-Feng Tian}, title = {Monotonicity and complete monotonicity of some functions involving the modified {Bessel} functions of the second kind}, journal = {Comptes Rendus. Math\'ematique}, pages = {217--235}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.399}, language = {en}, }
TY - JOUR AU - Zhong-Xuan Mao AU - Jing-Feng Tian TI - Monotonicity and complete monotonicity of some functions involving the modified Bessel functions of the second kind JO - Comptes Rendus. Mathématique PY - 2023 SP - 217 EP - 235 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.399 LA - en ID - CRMATH_2023__361_G1_217_0 ER -
%0 Journal Article %A Zhong-Xuan Mao %A Jing-Feng Tian %T Monotonicity and complete monotonicity of some functions involving the modified Bessel functions of the second kind %J Comptes Rendus. Mathématique %D 2023 %P 217-235 %V 361 %I Académie des sciences, Paris %R 10.5802/crmath.399 %G en %F CRMATH_2023__361_G1_217_0
Zhong-Xuan Mao; Jing-Feng Tian. Monotonicity and complete monotonicity of some functions involving the modified Bessel functions of the second kind. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 217-235. doi : 10.5802/crmath.399. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.399/
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