Results 21 to 30 of about 114 (80)

Certain Extension of the Hurwitz-Lerch Zeta Function and its Properties [PDF]

مجلّة جامعة عدن للعلوم الأساسيّة والتّطبيقيّة, 2020
The main object of this paper is to introduce a new extension of Hurwitz-Lerch Zeta function by using the extended Beta function given in [1]. Some recurrence relations, generating functions and integral representations are derived for that new extension.
Ahmed Ali Al-Gonah, Waleed Khadher Mohammed   +1 more
doaj   +2 more sources

INCOMPLETE EXTENDED HURWITZ-LERCH ZETA FUNCTIONS AND ASSOCIATED PROPERTIES

Communications of the Korean Mathematical Society, 2017
Rakesh K. Parmar, Ram K. Saxena
openaire   +4 more sources

Extended Levett trigonometric series. [PDF]

PLoS One
An extension of two finite trigonometric series is studied to derive closed form formulae involving the Hurwitz-Lerch zeta function. The trigonometric series involves angles with a geometric series involving the powers of 3.
Reynolds R.
europepmc   +2 more sources

Analytic continuation of the extended Hurwitz-Lerch Zeta function

Sarajevo Journal of Mathematics, 2013
The object of this paper is to investigate the analytic continuation and asymptotic expansions for families of the generalized Hurwich-Lerch Zeta functions defined by Srivastava et al. [24]. The result obtained is of general character and includes, as special cases, the same fashion results the Gauss hypergeometric function, the generalized ...
Ram K. Saxena, Tibor K. Pogany
  +6 more sources

Aspects of the screw function corresponding to the Riemann zeta‐function

Journal of the London Mathematical Society, Volume 108, Issue 4, Page 1448-1487, October 2023., 2023
Abstract We introduce a screw function corresponding to the Riemann zeta‐function and study its properties from various aspects. Typical results are several equivalent conditions for the Riemann hypothesis in terms of the screw function. One of them can be considered an analog of so‐called Weil's positivity or Li's criterion.
Masatoshi Suzuki
wiley   +1 more source

Some Weighted Sum Formulas for Multiple Zeta, Hurwitz Zeta, and Alternating Multiple Zeta Values

Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021
We perform a further investigation for the multiple zeta values and their variations and generalizations in this paper. By making use of the method of the generating functions and some connections between the higher‐order trigonometric functions and the Lerch zeta function, we explicitly evaluate some weighted sums of the multiple zeta, Hurwitz zeta ...
Yuan He, Zhuoyu Chen, Li Guo
wiley   +1 more source

The Mellin Transform of Logarithmic and Rational Quotient Function in terms of the Lerch Function

Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021
Upon reading the famous book on integral transforms volume II by Erdeyli et al., we encounter a formula which we use to derive a Mellin transform given by ∫0∞xm−1logkax/β2+x2γ+xdx, where the parameters a, k, β, and γ are general complex numbers. This Mellin transform will be derived in terms of the Lerch function and is not listed in current literature
Robert Reynolds, Allan Stauffer, Barbara Martinucci   +2 more
wiley   +1 more source

Analytical properties of the Hurwitz–Lerch zeta function

Advances in Difference Equations, 2020
In the present paper, we aim to extend the Hurwitz–Lerch zeta function Φ δ , ς ; γ ( ξ , s , υ ; p ) $\varPhi _{\delta ,\varsigma ;\gamma }(\xi ,s,\upsilon ;p)$ involving the extension of the beta function (Choi et al. in Honam Math. J.
Raghib Nadeem, Talha Usman, Kottakkaran Sooppy Nisar, Dumitru Baleanu   +3 more
doaj   +1 more source

Non-Zero Order of an Extended Temme Integral [PDF]

, 2022
A new three-dimensional integral containing f(x,y,z)Iv(xα) is derived where Iv(xα) is the Modified Bessel Function of the first kind and the integral is taken over the infinite cubic space 0<x<∞,0<y<∞,0<z<∞.
Robert Reynolds, Allan Stauffer
core   +1 more source

Extended Ohtsuka–Vălean Sums [PDF]

, 2022
The Ohtsuka–Vălean sum is extended to evaluate an extensive number of trigonometric and hyperbolic sums and products. The sums are taken over finite and infinite domains defined in terms of the Hurwitz–Lerch zeta function, which can be ...
Robert Reynolds, Allan Stauffer
core   +1 more source