On a general inequality related to the generalized-Euler-constant function

نویسندگان
چکیده

منابع مشابه

On generalized Hermite-Hadamard inequality for generalized convex function

In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.

متن کامل

The Generalized-Euler-Constant Function γ(z) and a Generalization of Somos’s Quadratic Recurrence Constant

We define the generalized-Euler-constant function γ(z) = ∑∞ n=1 z n−1 ( 1 n − log n+1 n ) when |z| ≤ 1. Its values include both Euler’s constant γ = γ(1) and the “alternating Euler constant” log 4 π = γ(−1). We extend Euler’s two zeta-function series for γ to polylogarithm series for γ(z). Integrals for γ(z) provide its analytic continuation to C − [1,∞). We prove several other formulas for γ(z...

متن کامل

A more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function

By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved. The more accurate equivalent forms, the operator expressions with the norm, the rever...

متن کامل

Padé approximant related to inequalities involving the constant e and a generalized Carleman-type inequality

Based on the Padé approximation method, in this paper we determine the coefficients [Formula: see text] and [Formula: see text] ([Formula: see text]) such that [Formula: see text] where [Formula: see text] is any given integer. Based on the obtained result, we establish new upper bounds for [Formula: see text]. As an application, we give a generalized Carleman-type inequality.

متن کامل

Vacca-Type Series for Values of the Generalized Euler Constant Function and its Derivative

We generalize well-known Catalan-type integrals for Euler’s constant to values of the generalized Euler constant function and its derivatives. Using generating functions appearing in these integral representations, we give new Vacca and Ramanujan-type series for values of the generalized Euler constant function and Addison-type series for values of the generalized Euler constant function and it...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Mathematical Inequalities

سال: 2020

ISSN: 1846-579X

DOI: 10.7153/jmi-2020-14-38