WebWe examine the exponentially improved asymptotic expansion of the Hurwitz zeta function ζ ( s , a ) for large complex values of a , with s regarded as a parameter. It is shown that an infinite number of subdominant exponential terms switch on … WebThe latter, equivalent to the functional equation of the non-holomorphic Eisenstein series on , admits a beautiful generalization of the form , that is, one can superimpose theta structure on it. Recently, a modular relation involving infinite series of …

A Quadruple Integral Involving Chebyshev Polynomials Tn(x): …

WebWe examine the improved infinite sum of the incomplete gamma function for large values of the parameters involved. We also evaluate the infinite sum and equivalent Hurwitz-Lerch zeta function at special values and produce a table of results for easy reading. Almost all Hurwitz-Lerch zeta functions have an asymmetrical zero distribution. Web23 de may. de 2024 · Real zeros of Hurwitz zeta-functions and their asymptotic behavior in the interval Kenta Endo, Yuta Suzuki Let , and be the Hurwitz zeta-function. Recently, …cyber theft news

Limiting Values and Functional and Difference Equations

WebWe introduce an explicit formula for a reciprocal sum related to the Riemann zeta function at s=6, and pose one question related to a computational formula for larger values of s. Web[2] that the Hurwitz zeta-function ζ(s;α)satisfies the analogue of Voronin’s univer-sality theorem whenever α is rational or transcendental. It appears that for every such α = 1 2,1, …WebIt appears that the only known representations for the Riemann zeta function ((z) in terms of continued fractions are those for z = 2 and 3. Here we give a rapidly converging continued-fraction expansion of ((n) for any integer n > 2. This is a special case of a more general expansion which we have derived for the polylogarithms of order n, n > 1, by using the …cyber theology