On a Conjecture of Alzer, Berg, and Koumandos
Mathematics, 2020 In this paper, we find a solution of an open problem posed by Alzer, Berg, and Koumandos: determine ( α , m ) ∈ R + × N such that the function x α | ψ ( m ) ( x ) | is completely monotonic on ( 0 , ∞ ) , where ψ (
Ladislav Matejíčka
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Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions [PDF]
Mathematical Problems in Engineering, 2020 In recent years, much attention has been paid to the role of degenerate versions of special functions and polynomials in mathematical physics and engineering. In the present paper, we introduce a degenerate Euler zeta function, a degenerate digamma function, and a degenerate polygamma function.
Fuli He +3 more
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General infinite series evaluations involving Fibonacci numbers and the Riemann zeta function
Математичні Студії, 2021 The purpose of this paper is to present closed forms for various types of infinite series involving Fibonacci (Lucas) numbers and the Riemann zeta function at integer arguments.
R. Frontczak, T. Goy
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On certain properties and expansions of zeta matrix function, digamma matrix function and polygamma matrix function [PDF]
, 2020 We introduce the generalized zeta matrix function, digamma matrix function and polygamma matrix function. We obtain the regions of convergence of these matrix functions, some recurrence relations and their integral representations.
Sahai, Vivek, Dwivedi, Ravi
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Pole decomposition of BFKL eigenvalue at zero conformal spin and the real part of digamma function [PDF]
, 2023 We consider the powers of leading order eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov~(BFKL) equation at zero conformal spin. Using reflection identities of harmonic sums we demonstrate how involved generalized polygamma functions are introduced by ...
Joubat, Mohammad +2 more
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A modular relation involving a generalized digamma function and asymptotics of some integrals containing Ξ(t) [PDF]
, 2022 A modular relation of the form $F(\alpha, w)=F(\beta, iw)$, where $i=\sqrt{-1}$ and $\alpha\beta=1$, is obtained. It involves the generalized digamma function $\psi_w(a)$ which was recently studied by the authors in their work on developing the theory of
Kumar, Rahul +3 more
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An inequality involving the gamma and digamma functions [PDF]
Journal of Applied Analysis, 2016 Abstract In the paper, the authors establish an inequality involving the gamma and digamma functions and apply it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.
Qi, Feng, Guo, Bai-Ni
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Closed-form summations of certain hypergeometric-type series containing the digamma function [PDF]
, 2008 Recently, interesting novel summation formulae for hypergeometric-type series containing a digamma function as a factor have been established by Miller (2006 J. Phys. A: Math. Gen.
Cvijović, Đurđe
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Some series whose coefficients involve the value ζ(n) for $n$n odd
International Journal of Mathematics and Mathematical Sciences, 1989 By using two basic formulas for the digamma function, we derive a variety of series that involve as coefficients the values (2n+1), n=1,2,⋯, of the Riemann-zeta function.
L. R. Bragg
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Sharp bounds for a ratio of the q-gamma function in terms of the q-digamma function
Journal of Inequalities and Applications, 2021 In the present paper, we introduce sharp upper and lower bounds to the ratio of two q-gamma functions Γ q ( x + 1 ) / Γ q ( x + s ) ${\Gamma }_{q}(x+1)/{\Gamma }_{q}(x+s)$ for all real number s and 0 < q ≠ 1 $0< q\neq1$ in terms of the q-digamma function.
Faris Alzahrani +2 more
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