接下来要看zs讲义的Cauchy积型极限部分了,所以需要了解一下Gamma和Beta函数。因为上课没认真听,这里重新复习一下。 Beta函数: 这是它的定义 B(p,q)=\int^{1}_0x^{p-1}(1-x)^{q-1}dx \\ 这个函数在 p>0,q>…
引用格式:魏正元,郑小洋,苏翃. 借助 Gamma 函数和 Beta 函数快速积分[J]. 重庆理工大学学报(自然科学),2016(9):129 -132.Citation format:WEI Zheng-yuan,ZHENG Xiao-yang,SU Hong. Integrals Based on Gamma and Beta Function[J]. Journalof Chongqing University of Technology(Natural Science),2016(9):...
beta functionp/ pWe improve several results recently established by Dragomir et al. in (2000) for the Gamma and Beta functions. All we need is some clever applications of classical inequalities./pdoi:10.1155/JIA.2005.593Agarwal, RPElezovi?, N...
Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function, Ap...
0 (1.2) Various well-known formulas for Gamma function are also given in [6]. For example, ∞Γ(x) = sx e−sttx−1dt, x, s > 0. 0 The Beta function is given by (1.3) 1 B(x, y) = tx−1(1 − t)y−1dt, x > 0, y > 0, 0 and its connection to Gamma ...
摘要: In this note we present a method for obtaining a wide class of combinatorial identities. We give several examples, in particular, based on the Gamma and Beta functions. Some of them have already been considered by previously, and other are new....
It is obvious that the Beta function has the symmetry property B(α,β)=B(β,α),α>0,β>0, (2.2) and the following connection between the Beta and Gamma functions holds: B(α,β)=Γ(α)Γ(β)Γ(α+β),α>0,β>0, (2.3) where Γ(α)=∫0∞e−ttα−1dt,α>...
The Beta distribution is a special case of the Dirichlet distribution, and is related to the Gamma distribution. It has the probability distribution function: 这里。由于Beta分数是二项分布的參数p的概率分布, 所以x(即p)的取值范围为0 <= x <= 1 ...
Beta分布在统计学中是定义在[0,1]区间内的一种连续概率分布,有α和β两个参数。 其概率密度函数为: wiki_PDF 累计密度函数为: wiki_CDF 就PDF的公式而言,Beta分布于二项分布还是比较相似的: (图片来自于https://towardsdatascience.com/beta-distribution-intuition-examples-and-derivation-cf00f4db57af) ...
(self, alpha): from math import gamma from operator import mul from functools import reduce self._alpha = np.array(alpha) self._coef = gamma(np.sum(self._alpha)) / reduce(mul, [gamma(a) for a in self._alpha]) #reduce:sequence连续使用function def pdf(self, x): #返回概率密度函数...