Show that the expansion of the function f(x) = a2r+1 %3D in a series of Hermite polynomials of odd order is: (2r + 1)! H2n+1(x) 22r+1 r = 0, 1,2, ... %3D 22r+1 (2 n + 1)! (r – n)! n=0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Show that the expansion of the function
f (x) = x2r+1
%3D
in a series of Hermite polynomials of odd order is:
(2r + 1)!
22r+1
H2n+1(x)
(2 n + 1)! (r – n)!
x2r+1
r = 0,1, 2, ...
%3D
n=0
Transcribed Image Text:Show that the expansion of the function f (x) = x2r+1 %3D in a series of Hermite polynomials of odd order is: (2r + 1)! 22r+1 H2n+1(x) (2 n + 1)! (r – n)! x2r+1 r = 0,1, 2, ... %3D n=0
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