Exercies:1) Express the polynomial x3 + 2x? - 5x+ 2 in a series ofLaguerre polynomials.2) Prove that:d?- L„(0) = n (n– 1)dx3) Prove that:a)Lo(x) = 1b)L,(x) = -x +1c)L2(x)1(x²-4x +2)2!d)L3(x) =(-x + 9x? – 18x + 6)3!" = (x)*1e) L4(x) =(x*- 16x + 72x² – 96x + 24).

Given that, x3+2x2-5x+2 is polynomial We Know that formula for laguerre polynomial is,…

Answered: Exercies: 1) Express the polynomial x +…

Math

Advanced Math

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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Question

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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