2004•Unpublished venueRequires access
Exact Solutions > Ordinary Differential Equations > Second-Order Linear Ordinary Differential Equations > Legendre Equation, Special Case 1
E. Kamke
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Abstract
The functions Pn = Pn(x) can be conveniently calculated by the recurrence relations: P0(x) = 1, P1(x) =x, P2(x) = 1 (3x 2 -1), ::: , Pn+1(x) = 2n+1 n+1 xPn(x)n n+1 Pn-1(x). Three leading functions Qn = Qn(x) are: Q0(x) = 1 ln 1 + x 1 - x , Q1(x) = x 2 ln 1 + x 1 - x - 1, Q2(x) = 3x 2 - 1 4 ln 1 + x 1 - x 3 2 x.