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Question: Assume user-defined relation (simplification of Jacobi polynomials)

Question:Assume user-defined relation (simplification of Jacobi polynomials)

shce 15 Maple 2021
September 06 2021
2

Hello,

I wonder if it is possible to define my own relationships so they can be used later with simplify.

 

Actually, I would like Maple to simplify the following expression

int(JacobiP(n, a, b, x)*JacobiP(m, a, b, x)*(1 - x)^a*(1 + x)^b, x = -1 .. 1)

 

but I haven't been able to do so. Therefore, I was wondering if it is possible to define

int(JacobiP(n, a, b, x)*JacobiP(m, a, b, x)*(1 - x)^a*(1 + x)^b, x = -1 .. 1) = piecewise(n <> m, 0, n = m, 2^(a + b + 1)*GAMMA(n + a + 1)*GAMMA(n + b + 1)/((2*n + a + b + 1)*GAMMA(n + a + b + 1)*n!))

 

and use this relation in further simplification operations.

 

Thank you in advance,
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