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(1- 2xt + t?) = (x-t)(x,t) (1) at ag (1- 2xt + t) t g(x,t) (2) ax ag t= (x - t) ag at (3) ere g(x,t) is the generating function of Legendre's polynomials Use Eq. (1) to prove the recurrence relation: (n + 1) Pn+1 = x(2n + 1) P-n Pn-1

(1- 2xt + t?) = (x-t)(x,t) (1) at ag (1- 2xt + t) t g(x,t) (2) ax ag t= (x - t) ag at (3) ere g(x,t) is the generating function of Legendre's polynomials Use Eq. (1) to prove the recurrence relation: (n + 1) Pn+1 = x(2n + 1) P-n Pn-1

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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1- Prove the following relations: (1– 2xt + t?) ag = (x - t) g(x, t) at (1) ag (1- 2xt +t2)=t g(x,t) (2) ax ag ag (x - t) (3) at Where g(x, t) is the generating function of Legendre's polynomials 2- Use Eq. (1) to prove the recurrence relation: (n + 1) Pn+1 = x(2n + 1) P, – n Pa-1
Transcribed Image Text:1- Prove the following relations: (1– 2xt + t?) ag = (x - t) g(x, t) at (1) ag (1- 2xt +t2)=t g(x,t) (2) ax ag ag (x - t) (3) at Where g(x, t) is the generating function of Legendre's polynomials 2- Use Eq. (1) to prove the recurrence relation: (n + 1) Pn+1 = x(2n + 1) P, – n Pa-1
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