Completely monotonic functions related to the special functions

Authors

  • Mohammad Soueycatt
  • Abedalbaset Yonsoo
  • Ahmad Bekdash
  • Nabil Salman

Abstract

 

In this paper, we discuss the completely monotonic functions and their relation to some of the famous special functions such as (Gamma, Kumar, Parabolic cylinder, Gauss hypergeometric, MacDonald, Whittaker and Generalized Mittag-Leffler) function. In addition, the relationship of the completely monotonic integrations with absolute progress under conditions of convergence such as transformations (Hankel, Lambert, Stieltjes and Laplace).

We will found other modes of composite functions given in terms of non-negative power chains and integrative transformations of completely monotonic non-negative functions, the state of integrative transform functions with a homogeneous nucleus of the first order, and the logarithmically completely monotonic functions.

The importance of the row of completely monotonic functions that are associated with the transformation of the Stieltjes defined as a class of special functions regression functions. Some of the oscillations of these functions resulting from completely monotonic functions are not decreasing or convex, but most of them are completely monotonic functions.

References

MILLER, K.S. ; SAMKO, S.G.. A note on the complete monotonicity of the generalized Mittag-Leffler function. Real Anal. Exchange, 23:753–755, 2011.

SAIGON, M. ; KILBAS, A.A. Integral representations and complete monotonicity of various quotients of Bessel functions. Canada. J. Math., 29:1198–1207, 2009.

ISMAIL. M.E.H. Complete monotonicity of modified Bessel functions. Proc. Amer. Math. Soc, 108, 2013:353–361.

SCHNEIDER. W.R. MILLER. An infinitely divisible distribution involving modified Bessel functions. Proc. Amer. Math. Soc, 85, 2003:233–238.

ISMAIL. M.E.H. On Mittag- Leffler, type function and applications. Integer. Transf. and Special Functions, 7, 2004:97–112.

SCHNEIDER. W.R. Completely monotone generalized Mittag-Leffler functions. Expo. Math., 14, 2009:3–16, 201.

Andrews,G.E. Askey, R. Roy, R. Special Functions, Cambridge Univ. Press, Cambridge, 2004.

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Published

2018-12-23

How to Cite

1.
Soueycatt M, Yonsoo A, Bekdash A, Salman N. Completely monotonic functions related to the special functions. TUJ-BA [Internet]. 2018Dec.23 [cited 2024Apr.24];40(6). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/5711

Issue

Vol. 40 No. 6 (2018): العلوم الاساسية

Section

Articles

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