Comptes Rendus
no. 3
Analyse complexe
Inequalities Involving q-Analogue of Multiple Psi Functions
[Inégalités impliquant des q-analogues des fonction psi multiples]
Sourav Das1 
1 Department of Mathematics, National Institute of Technology Jamshedpur, Jharkhand-831014, India
Comptes Rendus. Mathématique, Volume 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.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.44
Classification : 33B15, 26D07, 26D15
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 
@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},
}
TY  - JOUR
AU  - Sourav Das
TI  - Inequalities Involving $q$-Analogue of Multiple Psi Functions
JO  - Comptes Rendus. Mathématique
PY  - 2020
SP  - 327
EP  - 332
VL  - 358
IS  - 3
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.44
LA  - en
ID  - CRMATH_2020__358_3_327_0
ER  - 
%0 Journal Article
%A Sourav Das
%T Inequalities Involving $q$-Analogue of Multiple Psi Functions
%J Comptes Rendus. Mathématique
%D 2020
%P 327-332
%V 358
%N 3
%I Académie des sciences, Paris
%R 10.5802/crmath.44
%G en
%F CRMATH_2020__358_3_327_0
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/

[1] Horst Alzer Sharp inequalities for the diagramma and polygamma functions, Forum Math., Volume 16 (2004) no. 2, pp. 181-221 | Zbl

[2] Horst Alzer Sub- and superadditive properties of Euler’s gamma function, Proc. Am. Math. Soc., Volume 135 (2007) no. 11, pp. 3641-3648 | DOI | MR | Zbl

[3] Horst Alzer; Stephan Ruscheweyh A subadditive property of the gamma function, J. Math. Anal. Appl., Volume 285 (2003) no. 2, pp. 564-577 | DOI | MR | Zbl

[4] Ernest W. Barnes The theory of the G-function, Q. J. Math, Volume 31 (1899), pp. 264-314 | Zbl

[5] Ernest W. Barnes On the theory of the multiple Gamma function, Cambr. Trans., Volume 19 (1904), pp. 374-439 | Zbl

[6] Necdet Batir Monotonicity properties of q-digamma and q-trigamma functions, J. Approx. Theory, Volume 192 (2015), pp. 336-346 | DOI | MR | Zbl

[7] Junesang Choi Multiple gamma functions and their applications, Analytic number theory, approximation theory, and special functions, Springer, 2014, pp. 93-129 | DOI | Zbl

[8] Won Sang Chung; Taekyun Kim; Toufik Mansour The q-deformed gamma function and q-deformed polygamma function, Bull. Korean Math. Soc., Volume 51 (2014) no. 4, pp. 1155-1161 | DOI | MR | Zbl

[9] Bai-Ni Guo; Feng Qi; Qiu-Ming Luo The additivity of polygamma functions, Filomat, Volume 29 (2015) no. 5, pp. 1063-1066 | MR | Zbl

[10] Frank H. Jackson On q-functions and a certain difference operator, Trans. R. Soc. Edinb., Volume 46 (1908) no. 2, pp. 253-281 | DOI

[11] Frank H. Jackson On a q-definite integrals, Quart. J., Volume 41 (1910), pp. 193-203 | Zbl

[12] Toufik Mansour; Armend Sh. Shabani Some inequalities for the q-digamma function, JIPAM, J. Inequal. Pure Appl. Math., Volume 10 (2009) no. 1, 12, 8 pages | MR | Zbl

[13] Simon N. M. Ruijsenaars On Barnes’ multiple zeta and gamma functions, Adv. Math., Volume 156 (2000) no. 1, pp. 107-132 | DOI | MR | Zbl

[14] H. M. Srivastava; Junesang Choi Zeta and q-Zeta functions and associated series and integrals, Elsevier, 2012 | Zbl

[15] Kimio Ueno; Michitomo Nishizawa The multiple gamma function and its q-analogue, Quantum groups and quantum spaces (Warsaw, 1995) (Banach Center Publications), Volume 40, Polish Academy of Sciences, 1995, pp. 429-441 | Zbl

[16] Marie-France Vignéras L’équation fonctionnelle de la fonction zeta de Selberg de groupe modulaire PSL(2;Z), Journees arithmétiques de Luminy (1978) (Astérisque), Volume 61, Société Mathématique de France, 1979, pp. 235-249 | Numdam | Zbl

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Inequalities involving the multiple psi function

Sourav Das

C. R. Math (2018)

A complete monotonicity property of the multiple gamma function

Sourav Das

C. R. Math (2020)