In this paper, we present a very accurate approximation for gamma function:\n\\begin{equation*} \\Gamma \\left( x+1ight) hicksim \\sqrt{2\\pi x}\\left(\n\\dfrac{x}{e}ight) ^{x}\\left( x\\sinh \\frac{1}{x}ight) ^{x/2}\\exp \\left(\n\\frac{7}{324}\\frac{1}{...
A duplication formula for the double gamma function Γ 2 来自 钛学术 喜欢 0 阅读量: 34 作者: J Choi 摘要: The double Gamma function had been defined and studied by Barnes [4], [5], [6] and others in about 1900, not appearing in the tables of the most well-known special ...
Asymptotic series for double zeta, double gamma, and Hecke L-functions Asymptotic expansions of the Barnes double zeta-functionformula hereand the double gamma-function [Gamma]2([alpha], (1, w)), with respect to the parameter ... MATSUMOTO,KOHJI - 《Mathematical Proceedings of the Cambridge ...
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Gamma Distribution Formula The probability density function for the gamma distribution is fk,θ(x)=xk−1e−x/θθkΓ(k) , x>0 where Γ(k) is the gamma function defined by Γ(k)=∫0∞tk−1e−t dt If k is an integer value, then the gamma function satisfies Γ(k)=(...
作者: J Malenfant 摘要: We derive expressions for the partition function p(n), with n in the form 7k+a, as (k+1)-dimensional determinants. 关键词: Mathematics - Number Theory 05A17 (Primary) 11P81 (Secondary DOI: 10.48550/arXiv.1106.2753 年份: 2011 收藏...
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Three classes of the stirling formula for the q-factorial function This technique that uses the multiplication formula (1.3) and Riemann sums was also developed by Mortici [8] to derive the Stirling's formula and to establish other interesting properties about the gamma function. A double inequal...
Explanation:Converts a number into a text representation in another base, for example, base 2 for binary. BESSELI Syntax:BESSELI(x, n) Explanation:Returns the modified Bessel function In(x). BESSELJ Syntax:BESSELJ(x, n) Explanation:Returns the Bessel function Jn(x). ...
Similarly to the rank one case, we want to prove that {\mathcal {Z}}_\text {tot}({{\hat{u}}};\xi ,\nu _R,a\omega ,b\omega ) = 0 for {{\hat{u}}} in (C.28). Thus, we construct an involutive map \gamma : m \mapsto m', acting on the set {\mathcal {M}} of...