Extension of complete monotonicity results involving the digamma function
Moroccan Journal of Pure and Applied Analysis, 2018 By using some analytical techniques, we prove a complete monotonicity property of a certain function involving the (p, k)-digamma function. Subsequently, we derive some inequalities for the (p, k)- digamma function.
Nantomah Kwara
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The sum of the series of reciprocals of the cubic polynomials with one zero and double non-zero integer root [PDF]
Mathematics in Education, Research and Applications, 2019 This contribution is a follow-up to author’s previous published papers and deals with the sum of the series of reciprocals of the cubic polynomials with one zero and double non-zero integer root.
Radovan Potůček
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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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A Rational Approximant for the Digamma Function [PDF]
Numerical Algorithms, 2003 Power series representations for special functions are computationally satisfactory only in the vicinity of the expansion point. Thus, it is an obvious idea to use instead Padé approximants or other rational functions constructed from sequence transformations.
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MONOTONICITY AND CONVEXITY PROPERTIES OF THE NIELSEN’S β-FUNCTION
Проблемы анализа, 2017 The Nielsen’s β-function provides a powerful tool for evaluating and estimating certain integrals, series and mathematical constants. It is related to other special functions such as the digamma function, the Euler’s beta function and the Gauss ...
Kwara Nantomah
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Complete monotonicity related to the k-polygamma functions with applications
Advances in Difference Equations, 2019 In this paper, we prove complete monotonicity of some functions involving k-polygamma functions. As an application of the main result, we also give new upper and lower bounds of the k-digamma function.
Li Yin, Jumei Zhang, XiuLi Lin
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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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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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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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