scholarly journals The parameterized-Euler-constant functionγα(z)

2013 ◽  
Vol 133 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Li-meng Xia
Keyword(s):  
Euler Constant

BETTER BOUNDS IN CHEN’S INEQUALITIES FOR THE EULER CONSTANT

2015 ◽  
Vol 92 (1) ◽  
pp. 94-97 ◽  
Author(s):  
JENICA CRINGANU
Keyword(s):  
Euler Constant

In this paper we improve the inequalities obtained by Chen in 2009 for the Euler–Mascheroni constant.

scholarly journals On a generalization of Euler constant in connection to di-Gamma function

2012 ◽  
Vol 21 (1) ◽  
pp. 13-20
Author(s):  
LASZLO BALOG ◽  
Keyword(s):  
Gamma Function ◽  
Euler’S Constant ◽  
Euler Constant ◽  
Appl Math ◽  
Euler's Constant

In this paper we study the sequences {xn}, {yn} defined for each n ≥ 1 by ... , in connection to Gamma and di-Gamma function. Our results generalize some previous ones in [Berinde, V. A new generalization of Euler’s constant, Creat. Math.Inform. 18 (2009), No. 2, 123–128] and [Sant ˆ am˘ arian, A., ˘ A generalization of Euler constant, Mediamira, Cluj-Napoca, 2008] and are inspired from the paper [Mortici, C., Improved convergence towards generalized Euler-Mascheroni constant, Appl. Math. Comput., 2009, doi: 10.1016/j.amc.2009.10.039].

scholarly journals Some new sequences that converge to a generalized Euler constant

2012 ◽  
Vol 25 (6) ◽  
pp. 941-945 ◽  
Author(s):  
Alina Sîntămărian
Keyword(s):  
Euler Constant

On applications for Mahler expansion associated with p-adic q-integrals

2019 ◽  
Vol 15 (01) ◽  
pp. 67-84 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Explicit Formula ◽  
Gamma Function ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Euler Polynomials ◽  
Symmetric Relation ◽  
Euler Constant ◽  
Basic Properties ◽  
Changhee Polynomials

In this paper, we primarily consider a generalization of the fermionic [Formula: see text]-adic [Formula: see text]-integral on [Formula: see text] including the parameters [Formula: see text] and [Formula: see text] and investigate its some basic properties. By means of the foregoing integral, we introduce two generalizations of [Formula: see text]-Changhee polynomials and numbers as [Formula: see text]-Changhee polynomials and numbers with weight [Formula: see text] and [Formula: see text]-Changhee polynomials and numbers of second kind with weight [Formula: see text]. For the mentioned polynomials, we obtain new and interesting relationships and identities including symmetric relation, recurrence relations and correlations associated with the weighted [Formula: see text]-Euler polynomials, [Formula: see text]-Stirling numbers of the second kind and Stirling numbers of first and second kinds. Then, we discover multifarious relationships among the two types of weighted [Formula: see text]-Changhee polynomials and [Formula: see text]-adic gamma function. Also, we compute the weighted fermionic [Formula: see text]-adic [Formula: see text]-integral of the derivative of [Formula: see text]-adic gamma function. Moreover, we give a novel representation for the [Formula: see text]-adic Euler constant by means of the weighted [Formula: see text]-Changhee polynomials and numbers. We finally provide a quirky explicit formula for [Formula: see text]-adic Euler constant.

New sequences that converge to a generalized Euler constant

Analysis ◽  
2012 ◽  
Vol 32 (2) ◽  
pp. 111-120
Author(s):  
Alina Sîntămărian
Keyword(s):  
Euler Constant

scholarly journals A Character on the Quasi-Symmetric Functions coming from Multiple Zeta Values

10.37236/821 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Michael E. Hoffman
Keyword(s):  
Mirror Symmetry ◽  
Symmetric Functions ◽  
Euler Class ◽  
Complex Manifolds ◽  
Multiple Zeta Values ◽  
Almost Complex Manifolds ◽  
Euler Constant ◽  
Multiple Zeta ◽  
Almost Complex ◽  
Zeta Values

We define a homomorphism $\zeta$ from the algebra of quasi-symmetric functions to the reals which involves the Euler constant and multiple zeta values. Besides advancing the study of multiple zeta values, the homomorphism $\zeta$ appears in connection with two Hirzebruch genera of almost complex manifolds: the $\Gamma$-genus (related to mirror symmetry) and the $\hat{\Gamma}$-genus (related to an $S^1$-equivariant Euler class). We decompose $\zeta$ into its even and odd factors in the sense of Aguiar, Bergeron, and Sottille, and demonstrate the usefulness of this decomposition in computing $\zeta$ on the subalgebra of symmetric functions (which suffices for computations of the $\Gamma$- and $\hat{\Gamma}$-genera).

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