i need the answer quickly 1-Prove the following relations:ag= (x – t) g(x, t)at(1 – 2xt + t?)(1)(1– 2xt + t2)g= t g(x, t)(2)agag= (x - t)ax(3)atWhere g(x, t) is the generating function of Legendre's polynomials2-Use Eq. (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: (1– 2xt + t?). dg = (x-t) g(x, t) at (1) og (1 – 2xt + t?) = t g(x, t) (2) ax ag = (x - t) at ag (3) ax Where g(x, t) is the generating function of Legendre's polynomials

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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.10: Partial Fractions

Problem 17E

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Question

i need the answer quickly

1-
Prove the following relations:
ag
= (x – t) g(x, t)
at
(1 – 2xt + t?)
(1)
(1– 2xt + t2)g
= t g(x, t)
(2)
ag
ag
= (x - t)
ax
(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 Pn-1

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