A q-analog of the gamma function defined by Gamma_q(x)=((q;q)_infty)/((q^x;q)_infty)(1-q)^(1-x), (1) where (x,q)_infty is a q-Pochhammer symbol (Koepf 1998, p. 26; Koekoek and Swarttouw 1998). The q-gamma function satisfies lim_(q->1^-)Gamma_q(x)=Ga
q -Gamma functionBasic hypergeometric functionLog-convexityLog-concavityGeneralized Turánianq -Hypergeometric identityThe paper studies logarithmic convexity and concavity of power series with coefficients involving q-gamma functions or q-shifted factorials with respect to a parameter contained in their ...
K ey wo r ds :Digamma function;q-an al ogue ;ratio of gam ma ( 上接 第 7 页 ) [2 ] McLean A R,Emery V C,Webster A,et a1.Population dynamics of HIV within an individual after treatment With Zidovudine [J ] .AIDS ,199 1,5(3 ) :485 —459. ...
q-Gamma functionInequalities and convexity properties known for the gamma function are extended to the q -gamma function, 0< q <1. Applying some classical inequalities for convex functions, we deduce monotonicity results for several functions involving the q -gamma function. Further applications to ...
Inequalities and convexity properties known for the gamma function are extended to the q -gamma function, 0< q <1. Applying some classical inequalities for convex functions, we deduce monotonicity results for several functions involving the q -gamma function. Further applications to the probability ...
We prove the following theorem for the q-gamma function Gamma(q)(x): (q;q)(infinity)(1-q)(1-x)(e)Sigma(infinity)(i=0)f(q(x+i)) 0, 0 0 and 0 < q < 1: (q;q)(infinity)(1-q)(1-x)(1/logq[psi q(x+log(3/4)/log q)+log(1-q)])(e) < Gamma(q)(x) < (q...
之商的一个不等式的 q 模拟,即 由上式计算的结果,根据引理 1 的结论,我们可以判断 g'(x)>0,也就是得到 g(x)是区间[0,1]上的单调递增函数.所以 f(x)也是区间[0,1]上的单调递 增函数,那么对于 f(x)就有 f(0)<f(x)<f(1),也就是 参考文献: [1]Artin E.The Gamma function[M].New ...
In Example 2, I’ll show you how to create a cumulative distribution function (CDF) of the gamma distribution. As in Example 1, we first need to create a sequence of quantiles:x_pgamma <- seq(0, 1, by = 0.02) # Specify x-values for pgamma function...
LIJingjing,SUNMei.CompletemonotonicitypropertiesoffunctionsinvolvingtheGammafunctionandtheirq,analogues[J].BasicSciencesJournalofTextileUniversities(2016)29(3):299,305. 0纺织高校基础科学学报第29卷 十分重要的作用.欧拉Gamma函数[1,2]定义为 n Γ(z)=lim→∞n!nz∏k=0(z+k),z≠0,-1,-2,…. 函数ψ...
The q-gamma function for x<0 来自 国家科技图书文献中心 喜欢 0 阅读量: 37 作者: DS Moak 摘要: In this paper we will state two analogues of the Bohr-Mollerup theorem for q >1. It turns out that the log convexity of f together with the initial condition and the functional equation...