Results 21 to 30 of about 936 (88)

Logarithmically complete monotonicity of a function related to the Catalan-Qi function

Acta Universitatis Sapientiae: Mathematica, 2016
In the paper, the authors find necessary and sufficient conditions such that a function related to the Catalan-Qi function, which is an alternative generalization of the Catalan numbers, is logarithmically complete monotonic.
Qi Feng, Guo Bai -Ni
doaj   +1 more source

Construction a new generating function of Bernstein type polynomials [PDF]

Applied Mathematics and Computation 218 (2011) 1072-1076, 2010
Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties this generating functions are given. By applying this generating function, not only derivative of these polynomials but also recurrence relations of these polynomials are found.
arxiv   +1 more source

A result regarding monotonicity of the Gamma function

Acta Universitatis Sapientiae: Mathematica, 2017
In this paper we analyze the monotony of the function ln Γ(x)ln (x2+τ)-ln (x+τ)${{{\rm{ln}}\,\Gamma ({\rm{x}})} \over {{\rm{ln}}\,({\rm{x}}^2 + \tau) - {\rm{ln}}\,({\rm{x}} + \tau)}}$ , for τ > 0.
Kupán Pál A., Márton Gyöngyvér, Szász Róbert   +2 more
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Uniqueness of nontrivially complete monotonicity for a class of functions involving polygamma functions [PDF]

, 2010
For $m,n\in\mathbb{N}$, let $f_{m,n}(x)=\bigr[\psi^{(m)}(x)\bigl]^2+\psi^{(n)}(x)$ on $(0,\infty)$. In the present paper, we prove using two methods that, among all $f_{m,n}(x)$ for $m,n\in\mathbb{N}$, only $f_{1,2}(x)$ is nontrivially completely ...
Abramowitz M., Bai-Ni Guo, Chen C.-P., Feng Qi, Guo B.-N., H. M. Srivastava, Ismail M. E.H., Mitrinović D. S., Qi F., Srivastava H. M., Widder D. V.   +10 more
core   +1 more source

Two asymptotic expansions for gamma function developed by Windschitl’s formula

Open Mathematics, 2018
In this paper we develop Windschitl’s approximation formula for the gamma function by giving two asymptotic expansions using a little known power series.
Yang Zhen-Hang, Tian Jing-Feng
doaj   +1 more source

Extended Riemann-Liouville type fractional derivative operator with applications

Open Mathematics, 2017
The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind.
Agarwal P., Nieto Juan J., Luo M.-J.
doaj   +1 more source

A simple proof of monotonicity for remainder of Stirling's formula [PDF]

arXiv, 2023
The monotonicity properties of remainder of Stirling's formula for the gamma function are simply obtained by using the integral transforms with series.
arxiv  

On generalized fractional integral with multivariate Mittag-Leffler function and its applications

Alexandria Engineering Journal, 2022
The fractional calculus (FC) has been extensively studied by researchers due to its vast applications in sciences in the last few years. In fractional calculus, multivariate Mittag–Leffler functions are considered the powerful extension of the classical ...
Amna Nazir, Gauhar Rahman, Asad Ali, Saima Naheed, Kottakkaran Soopy Nisar, Wedad Albalawi, Heba Y. Zahran   +6 more
doaj  

Umbral Methods and Harmonic Numbers

Axioms, 2018
The theory of harmonic-based functions is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
Giuseppe Dattoli, Bruna Germano, Silvia Licciardi, Maria Renata Martinelli   +3 more
doaj   +1 more source

Some New Application of Extended Wright Function

Abstract and Applied Analysis
MSC2020 Classification: 26A33, 33B15, 33C05, 65D20, 33E20 ...
Pallavi Sharma, Ekta Mittal, D. L. Suthar, Rajni Gupta   +3 more
doaj   +1 more source