On co-recursive associated Laguerre polynomials
The author gives an explicit formula, a generating function, the orthogonality measure and a fourth-order differential equation for the co-recursive associated Laguerre-polynomials (first replace \(n\) by \(n+c\) in the recurrence relation for the ordinary Laguerre-polynomials and then replace the first degree polynomial \(-(x-2c-\alpha -1)/(c+1)\) by \(-(x- \mu-2c-\alpha-1)/(c+1)\); \(c\) has to satisfy \((n+c)(n+c+\alpha)>0\) for \(n \geq 1\), the range for \(\mu \neq 0\) is not mentioned in the paper). Finally some limit cases are shown to lead to known results, thereby exhibiting the `umbrella function' of the polynomials considered.
scientific article; zbMATH DE number 540457
scientific article