A note on parameter derivatives of classical orthogonal polynomials

Abstract

Coefficients in the expansions of the form $\partial P_{n}(λ;z)}/\partialλ=\sum_{k=0}^{n}a_{nk}(λ)P_{k}(λ;z)$, where $P_n(\lambda ;z)$ is the $n$th classical (the generalized Laguerre, Gegenbauer or Jacobi) orthogonal polynomial of variable $z$ and $\lambda$ is a parameter, are evaluated. A method we adopt in the present paper differs from that used by Fröhlich [Integral Transforms Spec. Funct. 2 (1994) 253] for the Jacobi polynomials and by Koepf [Integral Transforms Spec. Funct. 5 (1997) 69] for the generalized Laguerre and the Gegenbauer polynomials.

8 pages, LaTeX; one reference added, some references updated

References in corpus (1)

• On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree

Cited by in corpus (4)

• On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree
• On Parameter Differentiation for Integral Representations of Associated Legendre Functions
• On the derivatives ${\partial }^2{P}_{\nu }(z)/\partial {\nu }^2$ and $\partial Q_{\nu }(z)/\partial \nu$ of the Legendre functions with respect to their degrees
• Representations for the parameter derivatives of some Koornwinder polynomials