Operational properties of a generalized Hermite transformation
Copyright policy )Operational properties of a generalized Hermite transformation
The author studies the generalized Hermite transformation \[ F(z)=\int^{\infty}_{0}f(t)H_ z(t)e^{-t^ 2}dt,\quad z\in {\mathbb{C}} \] on some original space, where \(H_ z\) is the Hermite function \(H_ z(t)=2^ zG(-z/2,1/2,t^ 2),\) arg(t)\(\geq 0\), \(z\in {\mathbb{C}}\), G is the confluent hypergeometric function of the second kind. Some convolution theorems and an inversion formula are obtained.
- Friedrich Schiller University Jena Germany
- DigiZeitschriften Germany
convolution theorems, 510.mathematics, Classical hypergeometric functions, \({}_2F_1\), inversion formula, Hermite transformation, Special integral transforms (Legendre, Hilbert, etc.), confluent hypergeometric function, Article
convolution theorems, 510.mathematics, Classical hypergeometric functions, \({}_2F_1\), inversion formula, Hermite transformation, Special integral transforms (Legendre, Hilbert, etc.), confluent hypergeometric function, Article
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