In this paper, the authors prove some inequalities and completely monotonic properties of polygamma functions. As an application, we give lower bound for the zeta function on natural numbers. Parti ...

In this paper we consider the summation of some Polygamma[n, f(x)] function from interval x equals to N_1 to interval x equals to N_2, where the value of f(x) along this interval includes some ...

In this paper, the authors prove some inequalities and completely monotonic properties of polygamma functions. As an application, we give lower bound for the zeta function on natural numbers.

The polygamma function of order $n$ is defined as the $n+1$th derivative of the gamma function, $\Gamma(z)$. $$ \Gamma(z) = \int_{0}^{\infty} t^{z-1}e^{-t} dt $$ The ...

We obtain a variety of series and integral representations of the digamma function \psi (a) ψ(a). These in turn provide representations of the evaluations \psi (p/q) ψ(p/q) at rational argument and ...

The connection is considered between integrals and series involving polygamma ψ (z) and zeta ζ (z, s) functions, Bernoulli Bn (z) and Euler En (z) polynomials, and Bernoulli Bn and Euler En numbers.

Special functions occupy a central role in mathematical analysis, bridging pure theory and practical application across diverse scientific fields. Their intrinsic properties—such as recurrence ...

Abstract: In this paper, an efficient statistical model, called generalized Gamma distribution (GΓD), for the empirical modeling of synthetic aperture radar (SAR) images is proposed. The GΓD forms a ...