V2EX generalized hypergeometric function

Generalized Hypergeometric Function

定义 Definition

广义超几何函数:一种重要的特殊函数,通常记作 \(_pF_q\)。它把常见的超几何函数推广到更一般的形式,广泛用于数学分析、物理(如量子力学)、工程与统计中的级数解与积分表示等问题。

发音 Pronunciation (IPA)

  • /dnrlazd haprdimtrk fkn/

例句 Examples

The generalized hypergeometric function is often written as pFq.
广义超几何函数常写作 \(_pF_q\)。

In mathematical physics, solutions to certain differential equations can be expressed in terms of the generalized hypergeometric function with specific parameters.
在数学物理中,某些微分方程的解可以用带特定参数的广义超几何函数来表示。

词源 Etymology

hypergeometric(超几何)一词来自“geometric(几何/几何级数)”的概念延伸:早期“geometric series(几何级数)”与“arithmetic(算术)”相对;“hyper-(超越、更高层次)”表示比普通几何级数更一般的级数结构。geeralized(广义的)说明它是在经典超几何函数基础上的进一步推广;function(函数)来自拉丁语 functio,表示“执行/作用”,在数学中指输入与输出的对应关系。

相关词 Related Words

文学与典籍 Literary Works

  • Higher Transcendental Functions(Bateman Manuscript Project / Bateman 手稿计划)
  • Handbook of Mathematical Functions(Abramowitz & Stegun)
  • *NIST Digital Library of Mathematical Functions (DLMF)*(NIST《数字化数学函数库》)
  • Special Functions(Andrews, Askey & Roy)
  • A Course of Modern Analysis(Whittaker & Watson)
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