6 citations · 22 across the 8 of their papers we have counts for
8 papers
The Riemann Hypothesis: A Qualitative Characterization of the Nontrivial Zeros of the Riemann Zeta Function Using Polylogarithms
Lazhar Fekih-Ahmed
We formulate a parametrized uniformly absolutely globally convergent series of (s) denoted by Z(s, x). When expressed in closed form, it is given by Z(s, x) = (s -- 1)(s) + 1…
On the Power Series Expansion of the Reciprocal Gamma Function
Lazhar Fekih-Ahmed
Using the reflection formula of the Gamma function, we derive a new formula for the Taylor coefficients of the reciprocal Gamma function. The new formula provides effective asympto…
A New Effective Asymptotic Formula for the Stieltjes Constants
Lazhar Fekih-Ahmed
We derive a new integral formula for the Stieltjes constants. The new formula permits easy computations as well as an exact approximate asymptotic formula. Both the sign oscillatio…
On Two Applications of Herschel's Theorem
Lazhar Fekih-Ahmed
As a first application of a very old theorem, known as Herschel's theorem, we provide direct elementary proofs of several explicit expressions for some numbers and polynomials that…
A Necessary Condition for a Nontrivial Zero of the Riemann Zeta Function via the Polylogarithmic Function
Lazhar Fekih-Ahmed
The author has found today an error in the denominator of the residue equation (4.5). This unfortunate mistake makes the conclusions and the title of the paper incorrect. The funct…
On Some Explicit Formulas for Bernoulli Numbers and Polynomials
Lazhar Fekih-Ahmed
We provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural defin…