Results 31 to 40 of about 813 (192)
Hermite-Hadamard-Type Integral Inequalities for Convex Functions and Their Applications
Mathematics, 2022 In this paper, we establish new generalizations of the Hermite-Hadamard-type inequalities. These inequalities are formulated in terms of modules of certain powers of proper functions. Generalizations for convex functions are also considered.
Hari M. Srivastava +2 more
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Completely monotonic degree of a function involving trigamma and tetragamma functions
AIMS Mathematics, 2020 Let $\psi(x)$ be the digamma function. In the paper, the author reviews backgrounds and motivations to compute complete monotonic degree of the function $\Psi(x)=[\psi'(x)]^2+\psi''(x)$ with respect to $x\in(0,\infty)$, confirms that completely monotonic
Feng Qi
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Monotonicity of Some Functions Involving The Beta Function [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2011 In this short paper the monotonicity of functions involving the Beta function is considered to be study by using a similar method given in [2] and [4].
Hanadi Saleem
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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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Two parameterized series representations for the digamma function
Applicable Analysis and Discrete Mathematics, 2022 Numerous series representations for various special functions and mathematical constants have been developed by many authors. The aim of this article is to establish two parameterized series representations for the digamma function that seem interesting due to their independence from the given parameters.
Alzer, Horst, Choi, Junesang
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Derivation of logarithmic integrals expressed in teams of the Hurwitz zeta function
AIMS Mathematics, 2020 In this paper by means of contour integration we will evaluate definite integrals of the form \begin{equation*} \int_{0}^{1}\left(\ln^k(ay)-\ln^k\left(\frac{a}{y}\right)\right)R(y)dy \end{equation*} in terms of a special function, where $R(y)$ is a ...
Robert Reynolds, Allan Stauffer
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Infinite family of approximations of the Digamma function
Mathematical and Computer Modelling, 2006 Let \(\textstyle \Psi(x):=\frac{\Gamma^{\prime}(x)}{\Gamma(x)}\) be the psi or digamma function. The authors construct an infinite number of approximations for \(\Psi(x)\), \(x\in (0,\infty)\), denoted as \(\{I_{a}, a\in[0,1]\}\), where \(I_{a}(x)=\ln(x+a)-\frac{1}{x}\).
Muqattash, Isa, Yahdi, Mohammed
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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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Some integrals involving k gamma and k digamma function [PDF]
Journal of the Egyptian Mathematical Society, 2020 AbstractIn this paper, some new integrals involving k gamma function and k digamma function have been established. An integral is established involving k gamma function, and its special values are discussed. Similarly, some new integrals have been established for k digamma function, and different elementary function is associated with it for different ...
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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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