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
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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).
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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