Inequalities for the Associated Legendre Functions
Inequalities for the Associated Legendre Functions
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相关勒让德函数的不等式
DOI：
10.1006/jath.1998.3207
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发表时间：
1998
影响因子：
0.9
通讯作者：
G. Lohöfer
中科院分区：
文献类型：
--
作者：
G. Lohöfer
本文讨论了第一类Legendre函数Pmn（x）对realx？1，1]和integersm，nare证明。一个关系推导，使我们能够推广已知的勒让德多项式Pn（x）的界限？P0 n（x）对于非零阶勒让德函数Pmn（x）.此外，还得到了A型（？，n，m）？maxx？？1，1]|（1？x2）？/ 2Pm（x）|? B（？，，n，m）的所有0？1/2和1？| M|? n.为什么？0和？= 1/2这些上限是已知结果的改进和简化。
In this paper bounds for the associated Legendre functions of the first kindPmn(x) for realx??1,1] and integersm,nare proved. A relation is derived that allows us to generalize known bounds of the Legendre polynomialsPn(x)?P0n(x) for the Legendre functionsPmn(x) of non-zero orderm. Furthermore, upper and lower bounds of the typeA(?,n,m)?maxx??1,1]|(1?x2)?/2Pmn(x)|?B(?,,n,m) are proved for all 0???1/2 and 1?|m|?n. For?=0 and?=1/2 these upper bounds are improvements and simplifications of known results.