On some generalisations of Laguerre polynomials. (Q2586610)

\[ \psi_{n,m}^{(\alpha)}(x) = e^{-\tfrac12 x}x^{\tfrac12\alpha} L_{n,m}^{(\alpha)}(x), \] wo \[ \begin{gathered} L_{n,m}^{(\alpha)}(x) = e^{\tfrac12 x} \sum_{h=0}^{n} \binom{n+\alpha}{n-h} \dfrac{(-x)^h}{h!} E_{m-h}(\tfrac12 x),\\ E_m(x) = e^{-x} - \sum_{h=0}^{m-1} \dfrac{(-x)^h}{h!}. \end{gathered} \] Angabe von Bedingungen dafür, daß das System \(\left\{\psi_{n,m}^{(\alpha)}(x)\right\}\) zu \(L_p(0,\infty)\) gehört.