Rediscovering the contributions of Rodrigues on the representation of special functions

Following the pressure of Hermite in 1865 and Heine in 1868, the name of Rodrigues was definitively associated to his famous representation given in 1815. In this paper, we precise the contribution of Rodrigues, proving that his formula not only generates the Legendre polynomials, but also special Gegenbauer polynomials and even the corresponding second kind functions, which are never mentioned. The links with Hildebrandt polynomials and with the Bell polynomials are also briefly examined.