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Inequalities Involving q-Analogue of Multiple Psi Functions
[Inégalités impliquant des q-analogues des fonction psi multiples]
Comptes Rendus. Mathématique, Tome 358 (2020) no. 3, pp. 327-332.

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.

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DOI : https://doi.org/10.5802/crmath.44
Classification : 33B15,  26D07,  26D15
@article{CRMATH_2020__358_3_327_0,
     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},
}
Sourav Das. Inequalities Involving $q$-Analogue of Multiple Psi Functions. Comptes Rendus. Mathématique, Tome 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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