A Combinatorial Interpretation of the Integral of the Product of Legendre Polynomials

J. Gillis, J. Jedwab, D. Zeilberger
1988 SIAM Journal on Mathematical Analysis  
Denote by P"(x) the Legendre polynomial of degree n and let I_ I",..."k: P"(x)...P"k(x)dx. I",...,n is written as a sum involving binomial coefficients and the sum is interpreted via a combinatorial model. This makes possible a combinatorial proof of a number of general theorems concerning I",..."k, not all of which seem analytically straightforward, including a direct combinatorial derivation of the known formula for Ia,b, and the expression of Ia,b,c,d as a simple finite sum. In addition, a
more » ... mber of apparently new combinatorial identities are obtained.
doi:10.1137/0519109 fatcat:adackwudanf63p6vka34vh2gta