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.

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 Operator Representation of Fermi-Dirac and Bose-Einstein Integral Functions with Applications

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
M. Aslam Chaudhry ◽  
Asghar Qadir
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Statistical Distributions ◽  
Operator Representation ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Quantum Statistical ◽  
Bose Einstein ◽  
Operator Representations ◽  
Class Of Functions

Fermi-Dirac and Bose-Einstein functions arise as quantum statistical distributions. The Riemann zeta function and its extension, the polylogarithm function, arise in the theory of numbers. Though it might not have been expected, these two sets of functions belong to a wider class of functions whose members have operator representations. In particular, we show that the Fermi-Dirac and Bose-Einstein integral functions are expressible as operator representations in terms of themselves. Simpler derivations of previously known results of these functions are obtained by their operator representations.

scholarly journals A (p,v)-Extension of Hurwitz-Lerch Zeta Function and its Properties

2018 ◽  
Author(s):  
Gauhar Rahman ◽  
KS Nisar ◽  
Shahid Mubeen
Keyword(s):  
Zeta Function ◽  
Beta Function ◽  
Integral Representations ◽  
Basic Properties ◽  
Mellin Transformation ◽  
Special Cases ◽  
Lerch Zeta Function ◽  
Derivative Formulas ◽  
Generating Relations

In this paper, we define a (p,v)-extension of Hurwitz-Lerch Zeta function by considering an extension of beta function defined by Parmar et al. [J. Classical Anal. 11 (2017) 81–106]. We obtain its basic properties which include integral representations, Mellin transformation, derivative formulas and certain generating relations. Also, we establish the special cases of the main results.

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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