scholarly journals Some approximations with Hurwitz zeta function

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 528-534
Author(s):  
Aykut Aygunes
Keyword(s):  
Zeta Function ◽  
Bernoulli Polynomials ◽  
Hurwitz Zeta Function ◽  
Asymptotic Formulae

In this paper, we focus on some approximations with Hurwitz zeta function. By using these approximations, we present some asymptotic formulae related to Hurwitz zeta function. As an application, we give two corollaries related to Bernoulli polynomials.

scholarly journals A New Family of Zeta Type Functions Involving the Hurwitz Zeta Function and the Alternating Hurwitz Zeta Function

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 233
Author(s):  
Daeyeoul Kim ◽  
Yilmaz Simsek
Keyword(s):  
Zeta Function ◽  
Generating Function ◽  
Bernoulli Polynomials ◽  
Hurwitz Zeta Function ◽  
New Class ◽  
Mellin Transformation ◽  
New Family ◽  
Euler Numbers And Polynomials ◽  
Lerch Zeta Function ◽  
Combinatorial Sums

In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by the second author. Applying the Mellin transformation to this generating function, we define a new class of zeta type functions, which is related to the interpolation functions of the Apostol–Bernoulli polynomials, the Bernoulli polynomials, and the Euler polynomials. This new class of zeta type functions is related to the Hurwitz zeta function, the alternating Hurwitz zeta function, and the Lerch zeta function. Furthermore, by using these functions, we derive some identities and combinatorial sums involving the Bernoulli numbers and polynomials and the Euler numbers and polynomials.

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.

scholarly journals Asymptotics to all orders of the Hurwitz zeta function

2018 ◽  
Vol 465 (1) ◽  
pp. 423-458 ◽  
Author(s):  
Arran Fernandez ◽  
Athanassios S. Fokas
Keyword(s):  
Zeta Function ◽  
Hurwitz Zeta Function

scholarly journals Relations among the Riemann Zeta and Hurwitz Zeta Functions, as Well as Their Products

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 754 ◽  
Author(s):  
A. C. L. Ashton ◽  
A. S. Fokas
Keyword(s):  
Zeta Function ◽  
Zeta Functions ◽  
Formal Proof ◽  
Hurwitz Zeta Function ◽  
Mean Square ◽  
Novel Approach ◽  
Starting Point ◽  
Lindelöf Hypothesis ◽  
Riemann Zeta ◽  
The Mean

In this paper, several relations are obtained among the Riemann zeta and Hurwitz zeta functions, as well as their products. A particular case of these relations give rise to a simple re-derivation of the important results of Katsurada and Matsumoto on the mean square of the Hurwitz zeta function. Also, a relation derived here provides the starting point of a novel approach which, in a series of companion papers, yields a formal proof of the Lindelöf hypothesis. Some of the above relations motivate the need for analysing the large α behaviour of the modified Hurwitz zeta function ζ 1 ( s , α ) , s ∈ C , α ∈ ( 0 , ∞ ) , which is also presented here.

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