Random triples
| Subject | Object |
|---|---|
| gptkb:Legendre_polynomial | \int_{-1}^1 P_m(x)P_n(x)dx = 2/(2n+1) \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} |
| 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:Hermite_polynomials | ∫_{-∞}^{∞} H_m(x) H_n(x) e^{-x^2} dx = 0 for m ≠ n |