The Lommel differential equation, named after Eugen von Lommel, is an inhomogeneous form of the Bessel differential equation: {\displaystyle z^ {2} {\frac {d^ {2}y} {dz^ {2}}}+z {\frac {dy} {dz}}+ (z^ {2}-\nu ^ {2})y=z^ {\mu +1}.} Solutions are given by the Lommel functions sμ,ν (z) and Sμ,ν (z), introduced by Eugen von Lommel (1880),

1880年数学家{{Link-en|隆梅尔|Eugen von Lommel}}首先给出隆梅尔方程的两个解，称为隆梅尔函数：

Lommel (Dutch pronunciation: [ˈlɔməl]) is a municipality and city [2] in the Belgian province of Limburg. Lying in the Kempen, it has about 34,000 inhabitants and is part of the arrondissement of Maaseik.

1880年数学家 隆梅尔 （英语：Eugen von Lommel） 首先给出隆梅尔方程的两个解，称为隆梅尔函数： 其中 Jν (z) 是第一类 贝塞尔函数， Yν (z) 是第二类贝塞尔函数。 Erdélyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz; Tricomi, Francesco G., Higher transcendental functions. Vol II (PDF), McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953 [2014-05-31], MR 0058756, （原始内容 存档 (PDF)于2011-07-14）

2 天之前 · There are several functions called "Lommel functions." One type of Lommel function appear in the solution to the Lommel differential equation and are given by

A Lommel polynomial R m,ν (z) is a polynomial in 1/z giving the recurrence relation + = (), (), + where J ν (z) is a Bessel function of the first kind. [1] They are given explicitly by , = = [/] ()!

1880年数学家 隆梅尔（英语：Eugen von Lommel） 首先给出隆梅尔方程的两个解，称为隆梅尔函数： 其中 Jν (z) 是第一类 贝塞尔函数， Yν (z) 是第二类贝塞尔函数。 Erdélyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz; Tricomi, Francesco G., Higher transcendental functions. Vol II (PDF), McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953 [2014-05-31], MR 0058756, （原始内容 存档 (PDF)于2011-07-14）

Lommel functions in two variables are also known. See also Anger function; Weber function; Struve function. Lommel functions were studied by E. Lommel [Lo]. E. Kamke, "Differentialgleichungen: Lösungen und Lösungsmethoden", 1. Gewöhnliche Differentialgleichungen, Chelsea, reprint (1947) Lommel function. Encyclopedia of Mathematics.

洛默尔多项式 [1] (Lommel polynomial)是广义超几何函数的一种。 从而定义出洛默尔多项式，并给出了它的具体表达式.由于在推导这两个关系式时只用到递推关系，因此，如果将第一类贝塞尔函数换成其他柱函数，这两个关系式仍然成立. 洛默尔多项式 (Lommel polynomial)是广义超几何函数的 …

2021年1月7日 · Mathematical function, suitable for both symbolic and numerical manipulation. S() satisfies the differential equation . For certain special arguments, ResourceFunction"LommelS" automatically evaluates to exact values. ResourceFunction"LommelS" can be evaluated to arbitrary numerical precision.