Refinements of some recent inequalities for certain special functions

Mochamed Akkouchi; Mochamed Amine Ighachane

Published: 2019-06-22

Vol. 33 (2019)

Refinements of some recent inequalities for certain special functions

Mochamed Akkouchi , Mochamed Amine Ighachane

Abstract

The aim of this paper is to give some refinements to several inequalities, recently etablished, by P.K. Bhandari and S.K. Bissu in [Inequalities via Hölder’s inequality, Scholars Journal of Research in Mathematics and Computer Science, 2 (2018), no. 2, 124–129] for the incomplete gamma function, Polygamma functions, Exponential integral function, Abramowitz function, Hurwitz-Lerch zeta function and for the normalizing constant of the generalized inverse Gaussian distribution and the Remainder of the Binet’s first formula for ln Γ(x).

Keywords:

Hölder’s inequalities , incomplete Gamma function , exponential integral function , Hurwitz-Lerch zeta function , Abramowitz function , Binet’s first formula

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Akkouchi, M., & Amine Ighachane, M. (2019). Refinements of some recent inequalities for certain special functions. Annales Mathematicae Silesianae, 33, 1–20. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13647

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References

1. M. Abramowitz and C.A. Stegun (eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing, Dover Publications, New York, 1972.
2. M. Akkouchi and M.A. Ighachane, Equivalence of Hölder's and Cauchy-Schwartz inequalities and application to extended gamma and beta functions. Submitted.
3. P.K. Bhandari and S.K. Bissu, Inequalities via Hölder's inequality, Scholars J. Res. Math. Comput. Sci. 2 (2018), no. 2, 124–129.
4. M.A. Chaudhry and S.M. Zubair, On a Class of Incomplete Gamma Functions with Applications, Chapman & Hall/CRC, Boca Raton, 2002.
5. A. Erdélyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Higher Transcendental Functions. Vol. I, Bateman Manuscript Project, McGraw-Hill Book Company, Inc., New York, 1953.
6. G.J.O. Jameson, The incomplete gamma functions, Math. Gaz. 100 (2016), no. 548, 298–306.
7. B. Jørgensen, Statistical Properties of the Generalized Inverse Gaussian Distribution, Lecture Notes in Statistics, 9, Springer-Verlag, New York, 1982.
8. C. Mortici, Turán-type inequalities for the gamma and polygamma functions, Acta Univ. Apulensis Math. Inform. 23 (2010), 117–121.
9. A.F. Nikiforov and V.B. Uvarov, Special Functions of Mathematical Physics, Birkhäuser Verlag, Basel, 1988. Google Scholar

Mochamed Akkouchi

akkm555@yahoo.fr

Affiliation:

Department of Mathematics, Faculty of Sciences-Semlalia, Cadi Ayyad University, Morroco Morocco

Mochamed Amine Ighachane

Affiliation:

Department of Mathematics, Faculty of Sciences-Semlalia, Cadi Ayyad University, Morroco Morocco

Vol. 33 (2019)
Published: 2019-07-18

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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