Exercies: 1) Express the polynomial x + 2x? - 5x + 2 in a series of Laguerre polynomials.
Exercies: 1) Express the polynomial x + 2x? - 5x + 2 in a series of Laguerre polynomials.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Exercies:
1) Express the polynomial x3 + 2x? - 5x+ 2 in a series of
Laguerre polynomials.
2) Prove that:
d?
- L„(0) = n (n– 1)
dx
3) Prove that:
a)
Lo(x) = 1
b)
L,(x) = -x +1
c)
L2(x)
1
(x²-4x +2)
2!
d)
L3(x) =(-x + 9x? – 18x + 6)
3!
" = (x)*1
e) L4(x) =(x*- 16x + 72x² – 96x + 24).
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