The Euler gamma-function Γ( s ) usually plays an important role in the theory of zeta-functions. It is a principal ingredient of functional equations, and therefore the behaviour of zeta-functions are influenced by properties of Γ( s ). For the convenience, in this chapter we recall some...
Elaborated the theory of higher transcendental functions by introducing the gamma function and the gamma density functions. Introduced a new method for solving 4th degree polynomials. Proved Newton's identities, Fermat's little theorem, Fermat's theorem on sums of two squares, and made distinct ...
gamma函数的求导会出现所谓的欧拉函数(phi),在一篇论文中我需要对好几个欧拉函数求值,结果不能理解,立即去google,发现了一个开源的python库可以用来计算欧拉函数 class eulerlib.numtheory.Divisors(maxnum=1000) Implements methods related to prime factors and divisors. Parameters: maxnum – Upper limit for the...
The aim of this paper is to develop analytic techniques to deal with certain monotonicity of combinatorial sequences. (1) A criterion for the monotonicity of the function $\sqrt[x]{f(x)}$ is given, which is a continuous analog for one result of Wang and
欧拉函数(Euler' totient function ) 欧拉函数(Euler' totient function ) Author: Jasper Yang School: Bupt 前言 gamma函数的求导会出现所谓的欧拉函数(phi),在一篇论文中我需要对好几个欧拉函数求值,结果不能理解,立即去google,发现了一个开源的python库可以用来计算欧拉函数...
About this article Cite this article Haruki, H. A new characterization of euler's gamma function by a functional equation.Aeq. Math.30, 300–301 (1986). https://doi.org/10.1007/BF02189936 Download citation Received17 January 1985 Issue DateDecember 1986 ...
function Fhat = flux(FL,FR,rhoL,rhouL,EL,rhoR,rhouR,ER,SR,SL) global gamma type UR = [rhoR;rhouR;ER]; UL = [rhoL;rhouL;EL]; switch type case 1 %% L-F Flux Fhat = 0.5*(FR + FL - max(abs(SR),abs(SL))*(UR - UL)); case 2 %% HLL Flux if SL >= 0 Fhat = FL;...
Sub- and Superadditive Properties of Euler\"s Gamma Function 来自 Semantic Scholar 喜欢 0 阅读量: 34 作者: Horst Alzer 摘要: Let α > 0 and 0 < c ≠ 1 be real numbers. The inequality $\\left(\\frac{\\Gamma (x+y+c)}{\\Gamma (x+y)}ight)^{1/\\alpha}<\\left(\\frac{\\...
behavior of the functions $heta(x)=\sqrt[x]{2 \zeta(x)\Gamma(x+1)}$ and $F(x)=\sqrt[x]{\frac{\Gamma(ax+b+1)}{\Gamma(c x+d+1)\Gamma(e x+f+1)}}$ is considered, where $\zeta(x)$ and $\Gamma(x)$ are the Riemann zeta function and the Euler Gamma function, ...
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