New Criteria for Existence of a Class of Generalized Euler-types Constants

Subject Areas : Statistics

M. H. EGHTESADI FARD ¹ , Mohammad Hadi Hooshmand ²

1 - Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
2 - Associate professor of mathematics/ Islamic Azad University

Received: 2018-04-12 Accepted : 2019-01-17 Published : 2019-02-20

Keywords: ثابت اویلر- ماسکورونی, ثابت‌های نوع اویلر, تابع گاما, جمع‌پذیری حدی توابع حقیقی,

Abstract :

One of the most important mathematical constants is Euler-Mascheroni constant that is the limit of the sequence -------------------------------- and is denoted by gamma. Some other developed constants known as Euler type constants are introduced in order to generalize the above constant. In the present paper, inspired by the functional sequence derivative of the limit summand of functions (introduced by Second the author in ) introduces a family of generalized Euler type constants, and a test for their convergence. Then the existence of such constants is proved, and it is shown that the existence test presented by J. Sandor that was published in Journal of Mathematical Analysis and Applications in is one of its corollaries, and that generalized Euler type constants include a vaster spectrum of them. Also, some relationships between the topic and the Gamma-type functions (a class of functions satisfied the difference functional equation ----------- will be considered.

References:

 

T. M. Apostol, Introduction to Analytic Number Theory, Springer, .

E. Artin, The Gamma Function, Holt Rhinehart & Wilson, New York ; Transl. by M. Butler ( ) from Einfuhrung un dfr Theorie der Gamma fonktion, Teubner, Leipzig, .

M. H. Hooshmand, Limit Summability of Real Functions, Real Analysis Exchange, .

M. H. Hooshmand, Another Look at the Limit Summability of Real Functions, J. Math. Ext.,

M. H. Hooshmand, Analytic­ Summ-ability of Real and Complex Functions, J. Contemp. Math. Anal., .

J. C. Lagarias, Eulers constant: Eulers Work and Modern Developments, Bulletin (New series) of the American Mathematical Society, vol. , No.

J. Sandor, On Generalized Euler Con-stants and Schlomilch-Lemonnier Type Inequalities, J. Math. Anal. Appl., .

R. J. Webster, Log-Convex Solutions to the Functional Equation -Type Functions, J. Math. Anal. Appl.,