Demonstration Of Legendre Polynomials As Solutions Of Legendre Differential Equations

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ABSTRACT

The Legendre polynomials have been derived using their generating function defined by 1 w(x, t) = (1 - 2xt + t 2 )-2 and recurrence relations developed by their use. These recurrence relations were employed to show that the polynomials are solutions of the Legendre second order non-homogenous linear ordinary differential equation.

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