Results 11 to 20 of about 5,395,506 (201)
THE MODULAR RELATION AND THE DIGAMMA FUNCTION
Kyushu Journal of Mathematics, 2011 In this paper we shall locate a class of fundamental identities for the gamma function and trigonometric functions in the chart of functional equations for the zeta- functions as a manifestation of the underlying modular relation. We use the beta-transform but not the inverse Heaviside integral.
CHAKRABORTY, K. +2 more
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Some results on the digamma function [PDF]
Applied Mathematics & Information Sciences, 2013 The digamma function is defined for x > 0 as a locally summable function on the real line by ˆ(x) = i∞ + Z 1 0 e it i e ixt 1 i e it dt: In this paper we use the neutrix calculus to extend the definition for digamma function for the negative integers. Also we consider the derivatives of the digamma function for negative integers.
Biljana Tuneska, Ilija Jolevski
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New Inequalities for Gamma and Digamma Functions [PDF]
Journal of Applied Mathematics, 2014 By using the mean value theorem and logarithmic convexity, we obtain some new inequalities for gamma and digamma functions.
M. R. Farhangdoost, M. Kargar Dolatabadi
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New Approximation Formula of Digamma Function with Bounded Remainder
MathematicsThis study establishes the new approximation formula for the Digamma function ψ(s)=lns−12s−112ss2+θ(s ...
Mansour Mahmoud +2 more
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Sharp bounds for gamma and digamma function arising from Burnside's formula [PDF]
Journal of Numerical Analysis and Approximation Theory, 2010 The main aim of this paper is to improve the Burnside's formula for approximating the factorial function. We prove the complete monotonicity of a function involving the gamma function to establish new lower and upper sharp bounds for the gamma and ...
Cristinel Mortici
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On k-analogues of digamma and polygamma functions [PDF]
Journal of Classical Analysis, 2018 Summary: In this work, we obtain some integral representations of \(k\)-analogue of classical digammafunction \(\Psi(x)\). Then by using the concepts of neutrix and neutrix limit, we generalize the \(k\)-digamma function \(\Psi_k(x)\) and the \(k\)-polygamma function \(\Psi_k^{(r)}(x)\) for all real values of \(x\), \(r\in \mathbb N\) and \(k>0\). Also,
Yıldırım, Emrah, Ege, İncı
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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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Pole decomposition of BFKL eigenvalue at zero conformal spin and the real part of digamma function [PDF]
, 2023 We 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 ...
Joubat, Mohammad +2 more
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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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Computation of the Gamma, Digamma, and Trigamma Functions [PDF]
SIAM Journal on Numerical Analysis, 1994 This paper gives an approximation for gamma function that, while different, has the same form as Lanczos one. Both approximations correct Stirling's approximation with contributions from the gamma function's poles a require \(O (-\log \varepsilon)\) time independent of \(z\) to calculate \(z!\) with \(a\) relative error \(\varepsilon\).
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