Question: Differentiating (13) with respect to u, using (13) in the resulting formula, and comparing coefficients of u n , obtain the Bonnet recursion. where n

Differentiating (13) with respect to u, using (13) in the resulting formula, and comparing coefficients of uⁿ, obtain the Bonnet recursion.

where n = 1, 2, . . . . This formula is useful for computations, the loss of significant digits being small (except near zeros). Try (14) out for a few computations of your own choice.

(n + 1)Pn+1(x) = (2n + 1)xP,(x) npn-1(x),

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