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Consider the Laguerre polynomials defined on the interval [0, ∞o) obeying the orthogonality relations f dx e-Ln(x)Lm(x) = (n!)√n,m Evaluate the integral (65² o dx e-xL₁(x) L₁(x) using the recurrence relation Ln+1(x) − (2n +1 − x) Ln(x) + n² Ln_1(x). Hint: Write L5(x) or xL6(x) in terms of Laguerre polynomials only.

Consider the Laguerre polynomials defined on the interval [0, ∞o) obeying the orthogonality relations f dx e-Ln(x)Lm(x) = (n!)√n,m Evaluate the integral (65² o dx e-xL₁(x) L₁(x) using the recurrence relation Ln+1(x) − (2n +1 − x) Ln(x) + n² Ln_1(x). Hint: Write L5(x) or xL6(x) in terms of Laguerre polynomials only.

Advanced Engineering Mathematics
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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Consider the Laguerre polynomials defined on the interval [0, ∞) obeying the orthogonality relations f dx e-Ln(x)Lm(x) = (n!)√n,m Evaluate the integral (61)² So dx e-¹xL5(x) L₁(x) using the recurrence relation Ln+1(x) − (2n + 1 − x) Ln(x) + n² Ln−1(x). Hint: Write L5(x) or xL₁(x) in terms of Laguerre polynomials only.
Transcribed Image Text:Consider the Laguerre polynomials defined on the interval [0, ∞) obeying the orthogonality relations f dx e-Ln(x)Lm(x) = (n!)√n,m Evaluate the integral (61)² So dx e-¹xL5(x) L₁(x) using the recurrence relation Ln+1(x) − (2n + 1 − x) Ln(x) + n² Ln−1(x). Hint: Write L5(x) or xL₁(x) in terms of Laguerre polynomials only.
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