a电介质宏观上不显电性 The dielectric medium on macroscopic does not reveal the electric properties[translate] a慢慢就明白了 Understood slowly[translate] a咨询引导区 Consultation guidance area[translate] a老师把同学们分成了两组来打篮球 Teacher divided into schoolmates two groups to hit the basketball...
GAMMA函数的简单证明 Γ函数(伽玛函数;gamma函数),是阶乘函数在实数与复数域上的扩展,是一个高等函数,无法用已知的指数、对数、三角函数的方法进行处理,要采用瑕积分的方式进行求解。 首先给出gamma函数的定义: 由定义可得 对方程进行变换 我们可以得到一个递回等式Γ(x+1) = xΓ(x),这也是gamma函数求解的依据...
incomplete gamma functiongamma functionpsi functionIn the article, we discuss the monotonicity properties of the function x→(1−e−axp)1/p/∫0xe−tpdt$xightarrow (1-e^{-ax^{p}} )^{1/p}/\\\int_{0}^{x}e^{-t^{p}}\\\,dt$ for a,p>0$a, p>0$ with p≠1$peq1$ on...
Monotonicity of the incomplete gamma function with applications 2016, Journal of Inequalities and Applications Monotonicity and inequalities involving the incomplete gamma function 2016, Journal of Inequalities and Applications Normalized Incomplete Beta Function: Log-Concavity in Parameters and Other Properties ...
Using these representations, we obtain a number of properties of the asymptotic expansions of the incomplete gamma function with large arguments, including explicit and realistic error bounds, asymptotics for the late coefficients, exponentially improved asymptotic expansions, and the smooth transition of ...
Evaluates the regularized lower incomplete gamma function: P ( x , a ) = γ ( a , x ) Γ ( a ) = 1 Γ ( a ) ∫ 0 x t a − 1 e − t d t The function can also be used to evaluate the regularized upper incomplete gamma function, which is defined as follows: Q ( ...
General properties of perturbation theoryOther nonperturbative techniquesUsing a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a ...
Gamma functionIncomplete Gamma functionsPathway fractional integral operatorIncompleteH-functionsMellin–Barnes type contourIncomplete Fox–Wright generalized hypergeometric functionsRiemann–Liouville fractional integral operatorsVery recently Srivastava et al. (Russ J Math Phys 25(1):116鈥 138, 2018) have ...
Letting P(u,x) denote the regularised incomplete gamma function, it is shown that for each α≥ 0, P(x,x+α) decreases as x increases on the positive real semi-axis, and P(x,x+α) converges to 1/2 as x tends to infinity. The statistical significance of these results is explored...
We used both the functional form of the terms involving the latent variables (e.g., ∇p) and the known properties of the latent fields (e.g., the forcing f being time-independent) to eliminate the dependence on both p and f from the regression problem. This would not have been ...