1- Prove the following relations:ag(1 – 2xt + t?)= (x - t) g(x, t)(1)atdg(1– 2xt + t?)=t g(x,t)(2)axag(x - t)atagt(3)axWhere g(x,t) is the generating function of Legendre's polynomials

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Answered: 1- Prove the following relations: ag (1…

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