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Inequalities for the Associated Legendre Functions

✍ Scribed by G. Lohöfer

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
260 KB
Volume
95
Category
Article
ISSN
0021-9045

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✦ Synopsis

In this paper bounds for the associated Legendre functions of the first kind P m n (x) for real x # [&1, 1] and integers m, n are proved. A relation is derived that allows us to generalize known bounds of the Legendre polynomials P n (x)#P 0 n (x) for the Legendre functions P m n (x) of non-zero order m. Furthermore, upper and lower bounds of the type A(:, n, m) max x # [&1, 1] |(1&x 2 ) :Â2 P m n (x)| B(:, n, m) are proved for all 0 : 1Â2 and 1 |m| n. For :=0 and :=1Â2 these upper bounds are improvements and simplifications of known results.

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