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A Certain Class of Approximations for the q-Digamma Function [PDF]
Rocky Mountain Journal of Mathematics, 2016 In this paper, we derive a class of approximations of the $q$-digamma function $\psi _q(x)$. The infinite family \[ I_a(x;q)=\log [x+a]_q+\frac {q^x\log q}{1-q^x}-\bigg (\frac 12-a\bigg )H(q-1)\log q, \] $a\in [0,1]$; $q>0$, can be used as approximating functions for $\psi _q(x)$, where $[x]_q=(1-q^x)/(1-q)$ and $H(\cdot )$ is the Heaviside step ...
Ahmed Salem
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Inequalities involving gamma and digamma functions
Studia Scientiarum Mathematicarum Hungarica, 2014We prove: (A) Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6 ...
Horst Alzer, Chao-Ping Chen
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Approximations for the Ratio of the Gamma Functions via the Digamma Function and Its Applications
Bulletin of the Brazilian Mathematical Society, New Series, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Han, Min +3 more
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Summations for certain series containing the digamma function
Journal of Physics A: Mathematical and General, 2006Apparently new summations in terms of well-known special functions are deduced for hypergeometric-type series containing a digamma function as a factor. As a by-product of this investigation new reduction formulae for the Kampe de Feriet function F0:2;12:1;0[x, x] are obtained.
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Monotonicity properties of \(q\)-digamma and \(q\)-trigamma functions
J. Approx. Theory, 2015The author proves certain new monotonicity properties and related inequalities involving Jackson's \(q\)-gamma, \(q\)-digamma and \(q\)-trigamma functions. For example, denoting by \(A(x)\) the square of digamma function, and \(B(x)\) the trigamma function, then for \(q>0\) the application \(B(x) + A(x) -\log q\cdot\sqrt{A(x)}\) is completely monotonic
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An addition type formula for the elliptic digamma function
Journal of Mathematical Analysis and Applications, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Q-Extensions of Some Estimates Associated With the Digamma Function
Journal of Approximation Theory, 2013Necdet Batir
exaly