Inequalities Involving $q$-Analogue of Multiple Psi Functions

Sourav Das

doi:10.5802/crmath.44

Analyse complexe

Inequalities Involving

q

-Analogue of Multiple Psi Functions
[Inégalités impliquant des q-analogues des fonction psi multiples]

Sourav Das ¹

¹ Department of Mathematics, National Institute of Technology Jamshedpur, Jharkhand-831014, India

Comptes Rendus. Mathématique, Volume 358 (2020) no. 3, pp. 327-332.

Résumé
Abstract

La dérivée logarithmique de la fonction gamma multiple est connue comme la fonction psi multiple. Dans ce travail, des q-analogues de fonctions psi multiples d’ordre n ont été considérés. Des propriétés de sous-additivité, superadditivité et convexité des dérivées d’ordre supérieur de ces fonctions en découlent. Certaines inégalités apparentées sont également obtenues pour ces fonctions et leur rapports.

Logarithmic derivative of the multiple gamma function is known as the multiple psi function. In this work $q$ -analogue of multiple psi functions of order $n$ have been considered. Subadditive, superadditive and convexity properties of higher order derivatives of these functions are derived. Some related inequalities for these functions and their ratios are also obtained.

Reçu le : 2019-08-18
Révisé le : 2020-02-13
Accepté le : 2020-03-24
Publié le : 2020-07-10

DOI : 10.5802/crmath.44

Classification : 33B15, 26D07, 26D15

Affiliations des auteurs :

Sourav Das ¹

¹ Department of Mathematics, National Institute of Technology Jamshedpur, Jharkhand-831014, India

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Sourav Das},
     title = {Inequalities {Involving} $q${-Analogue} of {Multiple} {Psi} {Functions}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {327--332},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {3},
     year = {2020},
     doi = {10.5802/crmath.44},
     language = {en},
}

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Sourav Das. Inequalities Involving $q$-Analogue of Multiple Psi Functions. Comptes Rendus. Mathématique, Volume 358 (2020) no. 3, pp. 327-332. doi : 10.5802/crmath.44. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.44/

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