Orthogonal Polynomials

Orthogonal Polynomials compares three families with their defining inner products. Legendre P_n uses weight 1 on [−1, 1]; Chebyshev T_n uses 1/√(1−x²) on [−1, 1]; and this tool uses the physicists’ Hermite H_n, with weight e^−x² on the real line. The plotted Hermite interval is only a viewing window. For n>0, the displayed adjacent-degree inner product should be close to zero when evaluated with the matching weight.