Let u be a Hermitian linear functional defined in the linear space of Laurent polynomials and F its corresponding CarathΓ©odory function. We establish the equivalence between a Riccati differential equation with polynomial coefficients for F , zAF = BF 2 + CF + D, and a distributional equation for u,
On the derivation of linkage equations for Laguerre function coefficients
β Scribed by M.H Diskin
- Book ID
- 115969949
- Publisher
- Elsevier Science
- Year
- 1977
- Tongue
- English
- Weight
- 259 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0022-1694
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A well-known generating function of the classical Laguerre polynomials was recently rederived probabillstically by Lee. In this paper, some other (presumably new) generating functions for the Laguerre polynomials are derived by means of probabillstic considerations. A direct (analytical) proof of ea
The Laguerre-Freud equations giving the recurrence coefficients fl~, y,, of orthogonal polynomials with respect to a D,,, semi-classical linear form are derived. D,,~ is the difference operator. The limit when to --~ 0 are also investigated recovering known results. Applications to generalized Meixn