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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
30.11. Legendre Polynomials, Legendre Functions, and Associated Legendre Functions 1539
30.11.2 Associated Legendre Functions with Integer Indices
and Real Argument
Formulas for associated Legendre functions. Differential equation.
The associated Legendre functions P
m
n
(x) of order m are defined by the formulas
P
m
n
(x) = (1 x
2
)
m/2
d
m
dx
m
P
n
(x), n = 1, 2, 3, . . . , m = 0, 1, 2, . . .
It is assumed by definition that P
0
n
(x) = P
n
(x).
Properties:
P
m
n
(x) = 0 if m > n, P
m
n
(x) = (1)
nm
P
m
n
(x).
The associated Legendre functions P
m
n
(x) have exactly n m real zeros, which lie on
the interval 1 < x < 1.
The associated Legendre functions P
m
n
(x) with low indices: ...
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Publisher Resources

ISBN: 9781466581494