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Is there a closed form for the quadruple inner product of Legendre Polynomials such as:

\begin{align} \int_{-1}^{1}P_k(x)P_l(x)P_m(x)P_n(x)dx \end{align}

I am aware of solutions for the triple inner product for Legendre Polynomials.

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1 Answer 1

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Take a look at "J. Miller, Formulas for Integrals of Products of Associated Legendre or Laguerre Functions, Mathematics of Computation, Vol. 17, No. 81 (Jan., 1963), pp. 84-87" and take $m=0$ and $r=4$.

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