Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 1

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Dirichlet beta

Sortuj według:

Ogranicz wyniki do:

On the complex magnitude of Dirichlet beta function

Kawalec A.

Computational Methods in Science and Technology

2020

Vol. 26, No. 1

21--28

In this article, we derive an expression for the complex magnitude of the Dirichlet beta function β(s) represented as a Euler prime product and compare with similar results for the Riemann zeta function. We also obtain formulas for β(s) valid for an even and odd kth positive integer argument and present a set of generated formulas for β(k) up to 11th order, including Catalan’s constant and compute these formulas numerically. Additionally, we derive a second expression for the complex magnitude of β(s) valid in the critical strip from which we obtain a formula for the Euler-Mascheroni constant expressed in terms of zeros of the Dirichlet beta function on the critical line. Finally, we investigate the asymptotic behavior of the Euler prime product on the critical line.