Orthogonal Polynomials - 18.30 Associated OP’s

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
18.30.E1	${\displaystyle{\displaystyle A_{n}A_{n+1}C_{n+1}>0}}$ A_{n}A_{n+1}C_{n+1} > 0	${\displaystyle{\displaystyle n\geq 0}}$	A[n]*A[n + 1]*C[n + 1] > 0	Subscript[A, n]*Subscript[A, n + 1]*Subscript[C, n + 1] > 0	Skipped - no semantic math	Skipped - no semantic math	-	-
18.30#Ex1	${\displaystyle{\displaystyle p_{-1}(x;c)=0}}$ p_{-1}(x;c) = 0		p[- 1](x ; c) = 0	Subscript[p, - 1][x ; c] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
18.30#Ex2	${\displaystyle{\displaystyle p_{0}(x;c)=1}}$ p_{0}(x;c) = 1		p[0](x ; c) = 1	Subscript[p, 0][x ; c] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
18.30.E3	${\displaystyle{\displaystyle p_{n+1}(x;c)=(A_{n+c}x+B_{n+c})p_{n}(x;c)-C_{n+c}p_{n-1}(x;c)}}$ p_{n+1}(x;c) = (A_{n+c}x+B_{n+c})p_{n}(x;c)-C_{n+c}p_{n-1}(x;c)		p[n + 1](x ; c) = (A[n + c]*x + B[n + c])*p[n](x ; c)- C[n + c]*p[n - 1](x ; c)	Subscript[p, n + 1][x ; c] == (Subscript[A, n + c]*x + Subscript[B, n + c])*Subscript[p, n][x ; c]- Subscript[C, n + c]*Subscript[p, n - 1][x ; c]	Skipped - no semantic math	Skipped - no semantic math	-	-