Exercies: 1) Express the polynomial xr + 2x2 - 5x + 2 in a series of Laguerre polynomials. 2) Prove that: d? dx? L„(0) = n; (n– 1) 3) Prove that:
Exercies: 1) Express the polynomial xr + 2x2 - 5x + 2 in a series of Laguerre polynomials. 2) Prove that: d? dx? L„(0) = n; (n– 1) 3) Prove that:
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Answer part 3 ( d and e )
Transcribed Image Text:Exercies:
1) Express the polynomial xr³ + 2x2 - 5x + 2 in a series of
Laguerre polynomials.
2) Prove that:
d?
dx? L„(0) = n;(n - 1)
3) Prove that:
а)
Lo(x) = 1
b)
L,(x) = -x+1
1
Ly(«) = «*² - 4x + 2)
c)
d)
L,(x) = (-x* + 9x? – 18x + 6)
9x²-18x +6)
3!
1
e) L,(x) =(x* – 16x + 72x2 - 96x +24).
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