Approximation of the dilogarithm function (original) (raw)

Applied Mathematics & Information Sciences, 2013

The digamma function is defined for x > 0 as a locally summable function on the real line by ψ(x) = −γ

Some completely monotonic functions involving polygamma functions and an application

Journal of Mathematical Analysis and Applications, 2005

By using the first Binet's formula the strictly completely monotonic properties of functions involving the psi and polygamma functions are obtained. As direct consequences, two inequalities are proved. As an application, the best lower and upper bounds of the n-th harmonic number are established.

Complete Monotonicity of Functions Related to Trigamma and Tetragamma Functions

Computer Modeling in Engineering & Sciences, 2022

In this paper, we study the completely monotonic property of two functions involving the function (x) = [ψ (x)] 2 + ψ (x) and deduce the double inequality x 2 + 3x + 3 3x 4 (2x + 1) 2 < (x) < 625x 2 + 2275x + 5043 3x 4 (50x + 41) 2 , x > 0 which improve some recent results, where ψ(x) is the logarithmic derivative of the Gamma function. Also, we deduce the completely monotonic degree of a function involving ψ (x).

Some completely monotonic functions involving the gamma and polygamma functions

Journal of The Australian Mathematical Society, 2006

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. As special cases of the established results, we deduce some new results concerning the p-digamma and the k-digamma functions. Our results are extensions of some previous results due to Qiu and Vuorinen, Mortici, and Merovci.

Approximation of the dilogarithm function (original) (raw)

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