%0 Journal Article
%T Differential recurrence formulae for orthogonal polynomials
%A Anton L. W. von Bachhaus
%J Le Matematiche
%D 1995
%I University of Catania
%X Part I - By combining a general 2nd-order linear homogeneous ordinary differential equation with the three-term recurrence relation possessed by all orthogonal polynomials, it is shown that sequences of orthogonal polynomials which satisfy a differential equation of the above mentioned type necessarily have a differentiation formula of the type: gn(x)Y'n(x)=fn(x)Yn(x)+Yn-1(x). Part II - A recurrence formula of the form: rn(x)Y'n(x)+sn(x)Y'n+1(x)+tn(x)Y'n-1(x)=0, is derived using the result of Part I.
%U http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/497