坎宁安函数

坎宁安函数又称为皮尔逊-坎宁安函数(Pearson-Cunningham function)是英国数学家坎宁安在1908年首先研究的特殊函数,[1],定义如下[2]

Cunningham function Maple animation

其中U为特里科米函数

坎宁安在是在用多变数扩展的埃奇沃斯级数,依几率密度函数来近似几率密度函数时用到坎宁安函数,坎宁安函数和一维或多维常系数的扩散方程有关[1]

坎宁安函数是下列微分方程的解

与其他函数的关系

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级数展开

 

脚注

  1. ^ 1.0 1.1 Cunningham (1908)
  2. ^ Cunningham, E. (1908), "The ω-Functions, a Class of Normal Functions Occurring in Statistics", Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character (The Royal Society) 81 (548): 310–331, doi:10.1098/rspa.1908.0085, ISSN 0950-1207, JSTOR 93061

参考文献

  • Cunningham, E., The ω-Functions, a Class of Normal Functions Occurring in Statistics, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character (The Royal Society), 1908, 81 (548): 310–331, ISSN 0950-1207, JSTOR 93061, doi:10.1098/rspa.1908.0085