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Journal of High Energy Physics, 2023 The Coon amplitude is a q-deformed generalization of the Veneziano amplitude exhibiting a semi-infinite sequence of poles that converge on an accumulation point, from which a branch cut emerges. A number of recent papers have provided compelling evidence
Christian Baadsgaard Jepsen
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Tokyo Journal of Mathematics, 2007 The author studies the Polygamma Functions defined by \[ \psi_n(\omega)=\frac{d^{n+1}}{d\omega^{n+1}}\left[ \ln \Gamma (\omega) \right], \] where \((n+\omega)\notin O_2,\) \(m\in N\cup\{ 0 \}, \) \(n\in N\) and \(O_2\) is the set of non-invertible elements in \(C_2=\{ a+bi_1 +ci_2 +di_1i_2: \, i_1^2=i_2^2=-1,\, a,b,c,d \in R \},\) \(\Gamma(\omega)\) --
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A harmonic mean inequality for the polygamma function [PDF]
Mathematical Inequalities & Applications, 2020 Summary: In this work, we discuss some new inequalities and a concavity property of the poly-gamma function \(\psi^{(n)}(x) =\frac{d^n}{dx^n} \psi(x)\), \(x>0\), where \(\psi(x)\) represents the digamma function (i.e., logarithmic derivative of the gamma function \(\Gamma(x)\)). Using these inequalities, the minimum value of the harmonic mean of \((-1)^
Das, Sourav, Swaminathan, A.
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Entropy, 2017 The paper devises a family of leptokurtic bell-shaped distributions which is based on the hyperbolic secant raised to a positive power, and bridges the Laplace and Gaussian laws on asymptotic arguments.
Mario Faliva, Maria Grazia Zoia
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Pole decomposition of BFKL eigenvalue at zero conformal spin and the real part of digamma function
Physics Letters BWe 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 ...
Mohammad Joubat +2 more
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Refinements of Some Recent Inequalities for Certain Special Functions
Annales Mathematicae Silesianae, 2019 The aim of this paper is to give some refinements to several inequalities, recently etablished, by P.K. Bhandari and S.K. Bissu in [Inequalities via Hölder’s inequality, Scholars Journal of Research in Mathematics and Computer Science, 2 (2018), no.
Akkouchi Mohamed +1 more
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Short Remarks on Complete Monotonicity of Some Functions
Mathematics, 2020 In this paper, we show that the functions x m | β ( m ) ( x ) | are not completely monotonic on ( 0 , ∞ ) for all m ∈ N , where β ( x ) is the Nielsen’s β -function and we prove the functions x m − 1
Ladislav Matejíčka
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Accurate approximations to the polygamma functions [PDF]
Quarterly of Applied Mathematics, 1979 Empirically obtained approximations to the polygamma functions ψ
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Monotonicity of a mean related to polygamma functions with an application
Journal of Inequalities and Applications, 2016 Let ψ n = ( − 1 ) n − 1 $\psi_{n}= ( -1 ) ^{n-1}$ ψ ( n ) $\psi^{ ( n ) }$ ( n = 0 , 1 , 2 , … $n=0,1,2,\ldots $ ), where ψ ( n ) $\psi^{ ( n ) }$ denotes the psi and polygamma functions.
Zhen-Hang Yang, Shen-Zhou Zheng
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Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.In this paper, we introduce a new two‐parameter deformation of the gamma function that generalizes some existing gamma‐type functions in the literature. We study properties of this function that depend on the parameters. We also prove some inequalities for the corresponding beta function and polygamma functions.
Anton Asare-Tuah +5 more
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