The Hermite function expansions of the Heaviside function. (English) Zbl 1315.33014
Summary: We calculate the coefficients of Hermite function expansions of the Heaviside functions, \(x^{p}_{+}\) with \(p\in \mathbb {N}\), \(\frac{1}{x\pm i0}\), the signum \(\operatorname{sgn}(x)\) and the principal value p.v.\(\frac{1}{x}\), explicitly.
MSC:
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 46F10 | Operations with distributions and generalized functions |
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