Refinements of Some Recent Inequalities for Certain Special Functions

• Autorzy: Mohamed Akkouchi , Mohamed Amine Ighachane
• Języki publikacji: EN

Abstrakty

EN

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 $\ln\Gamma(x)$. (original abstract)

Słowa kluczowe

EN

Mathematics; Mathematical functions; Mathematical statistics

PL

Matematyka; Funkcje matematyczne; Statystyka matematyczna

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2019
• Tom: 33
• Strony: 1--20

Twórcy

autor

Mohamed Akkouchi

• Cadi Ayyad University, Morocco

autor

Mohamed Amine Ighachane

• Cadi Ayyad University, Morocco

Bibliografia

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

Identyfikatory

DOI

10.2478/amsil-2019-0009