Inequalities Involving $q$-Analogue of Multiple Psi Functions

Sourav Das

doi:10.5802/crmath.44

Complex Analysis

Inequalities Involving

q

-Analogue of Multiple Psi Functions

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.

Abstract
Résumé

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.

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.

Received: 2019-08-18
Revised: 2020-02-13
Accepted: 2020-03-24
Published online: 2020-07-10

DOI: 10.5802/crmath.44

Classification: 33B15, 26D07, 26D15

Author's affiliations:

Sourav Das ¹

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

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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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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