V2EX gamma function

Gamma Function

定义 Definition

Gamma function(伽马函数)是数学中的一种特殊函数,记作 **Γ(x)**,用来把“阶乘”的概念从正整数推广到更广的实数与复数范围。对正整数 n,有 **Γ(n) = (n1)!**。(它在统计学、物理学与工程中也很常见。)

发音 Pronunciation (IPA)

/m fkn/

例句 Examples

The gamma function extends the factorial to non-integers.
伽马函数把阶乘推广到非整数。

In probability theory, the gamma function appears in the normalization constant of the gamma distribution and the beta function.
在概率论中,伽马函数会出现在伽马分布与贝塔函数的归一化常数里。

词源 Etymology

“Gamma”来自希腊字母 Γ(gamma)。之所以用这个名字,和早期数学家在研究这类推广阶乘的函数时采用希腊字母作记号有关;后来 Euler(欧拉)系统研究并推广了这一函数,使 Γ(x) 成为标准记法。“Function”来自拉丁语系词根,表示“起作用的关系/函数”。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Leonhard Euler 的相关论文与著作(如对 Γ 函数的系统研究与记号推广)
  • Thomas M. Apostol,《Calculus, Vol. 1 & 2》(微积分教材中常作为特殊函数出现)
  • E. T. Whittaker & G. N. Watson,《A Course of Modern Analysis》(现代分析/特殊函数经典著作)
  • Abramowitz & Stegun,《Handbook of Mathematical Functions》(数学函数手册中对伽马函数有专门条目)
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