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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 )
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).
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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