Results 31 to 40 of about 681 (108)
Bounds for the ratio of two gamma functions: from Wendel’s asymptotic relation to Elezović-Giordano-Pečarić’s theorem [PDF]
, 2009 In the expository review and survey paper dealing with bounds for the ratio of two gamma functions, along one of the main lines of bounding the ratio of two gamma functions, the authors look back and analyze some known results, including Wendel’s ...
Feng Qi (祁锋), Qiu-Ming Luo
semanticscholar +1 more source
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
Journal of Inequalities and Applications, 2013 A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of ...
Junesang Choi
semanticscholar +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. +2 more
doaj +1 more source
Construction a new generating function of Bernstein type polynomials
, 2010 Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties this generating functions are given.
Simsek, Yilmaz
core +1 more source
Asymptotic formulae associated with the Wallis power function and digamma function
, 2013 Let s,t be two given real numbers, s = t . We determine the coefficients c j(s,t) such that [ Γ(x+ t) Γ(x+ s) ]1/(t−s) ∼ exp ( ψ ( x+ ∞ ∑ j=0 c j(s,t)x− ) )) as x → ∞ , where ψ(x) = Γ′(x)/Γ(x) denotes the digamma function.
Chao Chen, N. Elezovic, Lenka Vuksic
semanticscholar +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
The best bounds in Gautschi's inequality
, 2000 Different approach to both Gautschi’s inequalities (1) and (2) is given. This results in obtaining the best upper bound in (1) and the best lower bound in (2). The main result is the proof of the convexity of the function [Γ(x+t)/Γ(x+s)]1/(t−s) for |t−s|
N. Elezovic, C. Giordano, J. Pečarić
semanticscholar +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
New Two Parameter Gamma Function
, 2020 In this paper we introduce the New/Generalized two parameter Gamma function and Pochhammer symbol. We named them, as Generalized p k Gamma Function and Generalized p k Pochhammer symbol and denoted as pΓk(x) and a p(x)n,k respectively.
Kuldeep Sing Gehlot
semanticscholar +1 more source