Rodrigues polynomial

Rodrigues formula for the Legendre polynomials may be derived as follows. Consider the expression... 

Rodrigues formula is of great use in the evaluation of definite integrals involving Legendre polynomials. Consider, for instance, the integral... 

Some features of the Legendre and Laguerre polynomials are discussed next. The Rodrigues formula for associated Legendre polynomials is... 

Finally, using the Rodrigues formula for associated Laguerre polynomials (cf. Abramowitz and Stegun, 1965 Powell and Craseman, 1961)... 

With a choice of constant such that P(. ) = 1, the Legendre polynomials are defined by Rodrigues formula ... 

Together with the Rodrigues formula (see e.g. Abramowitz and Stegun [1]) for Hermite polynomials the derivatives of the Gaussian function are given by... 

The Jacobi polynomials are given explicitly by the Rodrigues formula... 

Frey and Rodrigues [20] proposed a method for the explicit calculation of multi-component equilibria using I AST. They used a polynomial or Taylor series to approximate the relationship between K and However, their method has... 

In Section 2 we were able to derive a complete set of recursive identities for the new "anharmonic polyrotdals that are orthogonal on the real line with respect to the wei t function w=e3p(-x ). CXir future work will determine the family of second order differential equations satisfied by these polynomials. We would also like to inv tigate vhether some type of modified Rodrigues formula and a simple generating function exist. 

The associated or generalized Laguerre polynomials L x) [11,12] may be obtained from the Rodrigues expression... 

Before we go on to consider the use of Hermite Gaussians as basis functions for overlap distributions, let us establish the relationship between Hermite Gaussians and Hermite polynomials. From Section 6.6.6, we recall that the Hermite polynomials may be generated from the Rodrigues... 

The reader may wish to derive the recurrence relations for the Legendre, Laguerre and Hermite polynomials from the Rodrigues expressions (6.4.4), (6.5.1) and (6.6.29). ... 

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