scholarly journals A Hilbert integral inequality with Hurwitz zeta function

2013 ◽  
pp. 377-387 ◽  
Author(s):  
He Leping ◽  
Gao Mingzhe
Keyword(s):  
Zeta Function ◽  
Integral Inequality ◽  
Hurwitz Zeta Function ◽  
Hilbert Integral

scholarly journals A reverse Hardy–Hilbert-type integral inequality involving one derivative function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Qian Chen ◽  
Bicheng Yang
Keyword(s):  
Integral Inequality ◽  
Beta Function ◽  
Equivalent Form ◽  
Constant Factor ◽  
Weight Functions ◽  
Derivative Function ◽  
The Best Possible Constant ◽  
Type Integral ◽  
Hilbert Type ◽  
Hilbert Integral

AbstractIn this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.

On multiple Hurwitz zeta function of Mordell–Tornheim type

2021 ◽  
pp. 1-34
Author(s):  
Kazuhiro Onodera
Keyword(s):  
Zeta Function ◽  
Hurwitz Zeta Function ◽  
Multiple Zeta Function ◽  
Multiple Zeta ◽  
Second Derivatives ◽  
Positive Integers

We introduce a certain multiple Hurwitz zeta function as a generalization of the Mordell–Tornheim multiple zeta function, and study its analytic properties. In particular, we evaluate the values of the function and its first and second derivatives at non-positive integers.

scholarly journals A note on a certain class of functions related to Hurwitz zeta function and Lambert transform

2000 ◽  
Vol 31 (1) ◽  
pp. 49-56
Author(s):  
R. K. Raina ◽  
T. S. Nahar
Keyword(s):  
Zeta Function ◽  
Hurwitz Zeta Function ◽  
Multiple Series ◽  
Generating Relations ◽  
Class Of Functions

In this paper we obtain multiple-series generating relations involving a class of function $ \theta_{(p_n)}^{(\mu_n)}(s,a;x_1,\ldots,x_n)$ which are connected to the Hurwitz zeta function. Also, a new generalization of Lambert transform is introduced, and its relationship with the above class of functions further depicted.

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