O 0 & Y:1HW_Legengre1.pdfHomework No.31-Prove the following relations:ag= (x - t) g(x, t)at(1 - 2xt +t2).(1)(1 - 2xt + t2)ag= t g(x, t)(2)ag= (x - t)atag(3)dxWhere g(x, t) is the generating function of Legendre's polynomials2-Use Eg. (1) to prove the recurrence relation:(n + 1) Pn+1 = x(2n + 1) P - n Pn-1

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1- Prove the following relations: ag (1 – 2xt + t*) = (x -1) g(x, t) (1) ag (1 – 2xt + t2)=t g(x,t) (2) ag = (x - t) at ag əx (3) Where g(x, t) is the generating function of Legendre's polynomials

1- Prove the following relations: ag (1 – 2xt + t*) = (x -1) g(x, t) (1) ag (1 – 2xt + t2)=t g(x,t) (2) ag = (x - t) at ag əx (3) Where g(x, t) is the generating function of Legendre's polynomials

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Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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Question

O 0 & Y:1
HW_Legengre1.pdf
Homework No.3
1-
Prove the following relations:
ag
= (x - t) g(x, t)
at
(1 - 2xt +t2).
(1)
(1 - 2xt + t2)
ag
= t g(x, t)
(2)
ag
= (x - t)
at
ag
(3)
dx
Where g(x, t) is the generating function of Legendre's polynomials
2-
Use Eg. (1) to prove the recurrence relation:
(n + 1) Pn+1 = x(2n + 1) P - n Pn-1

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