Extensions of Rodrigues' formula for second kind solutions of hypergeometric equation
Benjamin Olinde Rodrigues is well known for basic formula in the representation of orthogonal polynomials.
In this talk a quick summary of his life and social environment will be presented. Moreover, we shall introduce a representation of Rodrigues type for the Second Kind Functions of all Classical Orthogonal Polynomials, including also classical discrete and their q-analogues.
This means that these functions can be written as the nth derivative of an explicit quantity as in the usual Rodrigues' formulas. In case of Jacobi Polynomials of degree n, the corresponding Function of Second Kind has
n-1, n or n+1 zeros depending of the values of the Jacobi parameters.
Andre Ronveaux (University of Namur, Belgium)
September 05, 2003