Question

The generating function for Legendre polynomials is 1.

(a) g(x, t) = 2xt 2

(b) g(x, t) = e

x/2

(c) g(x, t) = (1 - 2 xt + t-1/2​

Answer 1

Explanation:

Introduction

The Legendre polynomials can be alternatively given by the generating function ( 1 − 2 x z + z 2 ) − 1 / 2 = ∑ n = 0 ∞ P n ( x ) z n , but there are other generating functions.