The Experts below are selected from a list of 93 Experts worldwide ranked by ideXlab platform
Feng Qi - One of the best experts on this subject based on the ideXlab platform.
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complete monotonicity of a Polygamma Function plus the square of another Polygamma Function
arXiv: Classical Analysis and ODEs, 2009Co-Authors: Feng QiAbstract:For $m,n\in\mathbb{N}$, let $$f_{m,n}(x)=\psi^{(n)}(x)+\bigr[\psi^{(m)}(x)\bigl]^2$$ for $x>0$. In the present paper, we prove that $f_{1,2}(x)$ is the only nontrivial completely monotonic Function on $(0,\infty)$. Accurately, the Functions $f_{1,2}(x)$ and $f_{m,2n-1}(x)$ are completely monotonic on $(0,\infty)$, but the Functions $f_{m,2n}(x)$ for $(m,n)\ne(1,1)$ are not monotonic and does not keep the same sign on $(0,\infty)$.
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The Best Bounds in Kershaw's Inequality and Two Completely Monotonic Functions
2006Co-Authors: Feng QiAbstract:A new proof for monotonicity and convexity of a Function deduced from Kershaw’s inequality involving the Wallis’ Function about the Euler’s gamma Function is provided. The complete monotonicity results of two Functions involving the divided differences of the psi Function ψ and Polygamma Function ψ' are established.
Victor H Moll - One of the best experts on this subject based on the ideXlab platform.
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a generalized Polygamma Function
Integral Transforms and Special Functions, 2004Co-Authors: Olivier Espinosa, Victor H MollAbstract:We study the properties of a Function ψ(z, q) (the generalized Polygamma Function), intimately connected with the Hurwitz zeta Function and defined for complex values of the variables z and q, which is entire in the variable z and reduces to the usual Polygamma Function ψ(m)(q) for z a non-negative integer m, and to the balanced negaPolygamma Function ψ(−m)(q) introduced in Ref. [5] for z a negative integer −m. *E-mail: oliver.espinosa@fis.utfsm.cl
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a generalized Polygamma Function
arXiv: Classical Analysis and ODEs, 2003Co-Authors: Olivier Espinosa, Victor H MollAbstract:We study the properties of a Function $\psi(z, q)$ (the generalized Polygamma Function), intimately connected with the Hurwitz zeta Function and defined for complex values of the variables $z$ and $q$, which is entire in the variable $z$ and reduces to the usual Polygamma Function $\psi^{(m)}(q)$ for $z$ a non-negative integer $m$, and to the balanced negaPolygamma Function $\psi^{(-m)}(q)$ for $z$ a negative integer $-m$.
K S Kolbig - One of the best experts on this subject based on the ideXlab platform.
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the Polygamma Function ψ k x for x 14 and x 34
Journal of Computational and Applied Mathematics, 1996Co-Authors: K S KolbigAbstract:Abstract Expressions for the Polygamma Function ψ(k)(x) for the arguments x = 1 4 and x = 1 4 are given in terms of Bernoulli numbers, Euler numbers, the Riemann zeta Function for odd integer arguments, and the related series of reciprocal powers of integers β(m).
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the Polygamma Function p k x for x 1 4 and x 3 4
Journal of Computational and Applied Mathematics, 1996Co-Authors: K S KolbigAbstract:Expressions for the Polygamma Function ψ (k) (x) for the arguments x = 1/4 and x = 3/4 are given in terms of Bernoulli numbers, Euler numbers, the Riemann zeta Function for odd integer arguments, and the related series of reciprocal powers of integers β(m).
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the Polygamma Function ψ k x for x and x
Journal of Computational and Applied Mathematics, 1996Co-Authors: K S KolbigAbstract:Expressions for the Polygamma Function @j^(^k^)(x) for the arguments x=14 and x=14 are given in terms of Bernoulli numbers, Euler numbers, the Riemann zeta Function for odd integer arguments, and the related series of reciprocal powers of integers @b(m).
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The Polygamma Function Ψ (k) (x) for x=¼ and x=¾
Journal of Computational and Applied Mathematics, 1996Co-Authors: K S KolbigAbstract:Expressions for the Polygamma Function @j^(^k^)(x) for the arguments x=14 and x=14 are given in terms of Bernoulli numbers, Euler numbers, the Riemann zeta Function for odd integer arguments, and the related series of reciprocal powers of integers @b(m).
Kwara Nantomah - One of the best experts on this subject based on the ideXlab platform.
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complete monotonicity properties of a Function involving the Polygamma Function
arXiv: Classical Analysis and ODEs, 2018Co-Authors: Kwara NantomahAbstract:In this paper, we study completete monotonicity properties of the Function $f_{a,k}(x)=\psi^{(k)}(x+a) - \psi^{(k)}(x) - \frac{ak!}{x^{k+1}}$, where $a\in(0,1)$ and $k\in \mathbb{N}_0$. Specifically, we consider the cases for $k\in \{ 2n: n\in \mathbb{N}_0 \}$ and $k\in \{ 2n+1: n\in \mathbb{N}_0 \}$. Subsequently, we deduce some inequalities involving the Polygamma Functions.
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remarks on some inequalities for analogues of the Polygamma Function
Mathematical Sciences and Applications E-Notes, 2018Co-Authors: Kwara NantomahAbstract:The purpose of this study is twofold. The first is, to point out drawbacks of some recent results concerning analogues the Polygamma Function. The second is to resolve the drawbacks by providing improvements of the previous results.
Olivier Espinosa - One of the best experts on this subject based on the ideXlab platform.
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a generalized Polygamma Function
Integral Transforms and Special Functions, 2004Co-Authors: Olivier Espinosa, Victor H MollAbstract:We study the properties of a Function ψ(z, q) (the generalized Polygamma Function), intimately connected with the Hurwitz zeta Function and defined for complex values of the variables z and q, which is entire in the variable z and reduces to the usual Polygamma Function ψ(m)(q) for z a non-negative integer m, and to the balanced negaPolygamma Function ψ(−m)(q) introduced in Ref. [5] for z a negative integer −m. *E-mail: oliver.espinosa@fis.utfsm.cl
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a generalized Polygamma Function
arXiv: Classical Analysis and ODEs, 2003Co-Authors: Olivier Espinosa, Victor H MollAbstract:We study the properties of a Function $\psi(z, q)$ (the generalized Polygamma Function), intimately connected with the Hurwitz zeta Function and defined for complex values of the variables $z$ and $q$, which is entire in the variable $z$ and reduces to the usual Polygamma Function $\psi^{(m)}(q)$ for $z$ a non-negative integer $m$, and to the balanced negaPolygamma Function $\psi^{(-m)}(q)$ for $z$ a negative integer $-m$.