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How to stop Mathematica from using polynomial relations to simplify expressions

Mathematica Asked on January 26, 2021

I am making a table whose entries involve Jacobi polynomials, $P_n^{(alpha,beta)}(x)$. Each entry contains some expression polynomials as a function of $n$, i.e. the first entry will be some function of Jacobi polynomials with $n$ evaluated at zero, the next will have $n=1$ etc.

I need the first entry to be n=0. However this causes issues because Mathematica automatically replaces any derivatives of the Jacobi polynomials with a Jacobi polynomial $n-1$, according to eq. (14) here: https://mathworld.wolfram.com/JacobiPolynomial.html .

When I evaluate my functions, the elements for $n=0$ end up including Jacobi polynomials of the form JacobiP[-1,alpha,beta,x], which Mathematica cannot handle.

Is there any way to stop Mathematica from simplifying the derivatives of the polynomials, so that when I specify the value of $n$ I can evaluate the correct expression?

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