Orthogonal Polynomials - 18.2 General Orthogonal Polynomials

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
18.2.E1	${\displaystyle{\displaystyle\int_{a}^{b}p_{n}(x)p_{m}(x)w(x)\mathrm{d}x=0}}$ \int_{a}^{b}p_{n}(x)p_{m}(x)w(x)\diff{x} = 0	${\displaystyle{\displaystyle n\neq m}}$	int(p[n](x)* p[m](x)* w(x), x = a..b) = 0	Integrate[Subscript[p, n][x]* Subscript[p, m][x]* w[x], {x, a, b}, GenerateConditions->None] == 0	Failure	Failure	Successful [Tested: 300]	Successful [Tested: 300]
18.2.E2	${\displaystyle{\displaystyle\sum_{x\in X}p_{n}(x)p_{m}(x)w_{x}=0}}$ \sum_{x\in X}p_{n}(x)p_{m}(x)w_{x} = 0	${\displaystyle{\displaystyle n\neq m}}$	sum(p[n](x)* p[m](x)* w[x], x in X) = 0	Sum[Subscript[p, n][x]* Subscript[p, m][x]* Subscript[w, x], {x, X}, GenerateConditions->None] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
18.2.E3	${\displaystyle{\displaystyle\sum_{x\in X}p_{n}(x)p_{m}(x)w_{x}=0}}$ \sum_{x\in X}p_{n}(x)p_{m}(x)w_{x} = 0		sum(p[n](x)* p[m](x)* w[x], x in X) = 0	Sum[Subscript[p, n][x]* Subscript[p, m][x]* Subscript[w, x], {x, X}, GenerateConditions->None] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
18.2.E4	${\displaystyle{\displaystyle\sum_{x\in X}x^{2n}w_{x}<\infty}}$ \sum_{x\in X}x^{2n}w_{x} < \infty		sum((x)^(2*n)* w[x](<)*infinity, x in X)	Sum[(x)^(2*n)* Subscript[w, x][<]*Infinity, {x, X}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
18.2.E8	${\displaystyle{\displaystyle p_{n+1}(x)=(A_{n}x+B_{n})p_{n}(x)-C_{n}p_{n-1}(x)}}$ p_{n+1}(x) = (A_{n}x+B_{n})p_{n}(x)-C_{n}p_{n-1}(x)	${\displaystyle{\displaystyle n\geq 0}}$	p[n + 1](x) = (((k[n + 1])/(k[n]))*x + B[n])*p[n](x)- C[n]*p[n - 1](x)	Subscript[p, n + 1][x] == ((Divide[Subscript[k, n + 1],Subscript[k, n]])*x + Subscript[B, n])*Subscript[p, n][x]- Subscript[C, n]*Subscript[p, n - 1][x]	Skipped - no semantic math	Skipped - no semantic math	-	-