Random triples
| Subject | Object |
|---|---|
| gptkb:Hermite_polynomials | ∫_{-∞}^{∞} H_m(x) H_n(x) e^{-x^2} dx = 0 for m ≠ n |
| gptkb:Legendre_polynomial | \\int_{-1}^1 P_m(x)P_n(x)dx = 2/(2n+1) \\delta_{mn} |
| gptkb:Charlier_polynomials | \\sum_{x=0}^\\infty C_m(x;a)C_n(x;a)\\frac{a^x}{x!}e^{-a} = a^n n! \\delta_{mn} |
| gptkb:probabilists'_Hermite_polynomials | \\int_{-\\infty}^{\\infty} H_m(x) H_n(x) \\frac{e^{-x^2/2}}{\\sqrt{2\\pi}} dx = n! \\delta_{mn} |