The Polynomial of Mittag-Leffler.
The Polynomial of Mittag-Leffler.
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Mittag-Leffler 多项式。
DOI：
10.1073/pnas.26.8.491
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发表时间：
1940
影响因子：
11.1
通讯作者：
H. Bateman
中科院分区：
文献类型：
--
作者：
H. Bateman
两个圆的平行圆周。同样，一个双面图形也可以逐渐变成单面图形。特别地，如果s是一条平面曲线，则解显然是由它包围的平面的一部分。如果s位于一个闭凸曲面上，则S本质上是双侧的。函数v（M）、V（M）一般不一定在s上连续，因为s的某些点可能是导体电势V（M）的不规则边界点。在二维空间中，类似的问题在特殊情况下被认为是Koebe关于保角映射的一个著名定理的推广。P6lya和Szego认为这是一个问题，在超限直径的两点边界在平面上，其中的解决方案是部分加入他们。2我感谢教授Szego的citations3方面的问题，在飞机上。特别是Grotzsch演示的方法保形映射的唯一性的解决方案为任意有限数目的点在平面上。1.多项式gn（z）= 2zF（1-n，1-z; 2; 2）作为展开式（1 + t）（1-t）= 1 + Eg（z）tn，ItI <1（1）n = o2zetF（1-z; 2;-2t）= Eg-（z）t/（n-1）中的系数出现! (2)Mittag-Leffierl在研究线性齐次微分方程的积分和不变量的解析表示时，
parallel circumferences of the two circles. Similarly a two-sided figure may be made to change gradually into a one-sided one. In particular, if s is a plane curve the solution is evidently the portion of the plane enclosed by it. If s lies on a closed convex surface, S is essentially two-sided. The functions v(M), V(M) are in general not necessarily continuous on s, for some of the points of s may be irregular boundary points for the conductor potential V(M). In two dimensions a similar problem has been considered in particular cases as a generalization of a well-known theorem of Koebe on conformal mapping. P6lya and Szego consider it as a problem in transfinite diameter for a two point boundary in the plane, where the solution is the segment joining them.2 I am indebted to Professor Szego for the citations3 with respect to the problem in the plane. In particular Grotzsch demonstrates by methods of conformal mapping the uniqueness of the solution for an arbitrary finite number of points in the plane. 1. The polynomial gn(z) = 2zF(l-n, 1-z; 2; 2) occurs as a coefficient in the expansions (1 + t)(1-t) = 1 + Eg (z)tn, I t I < 1 (1) n = o 2zetF(1-z; 2;-2t) = Eg-(z)t /(n-1)! (2) n= 1 It was used by Mittag-Leffierl in a study of the analytical representation of the integrals and invariants of a linear homogeneous differential equa