Series Info:INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS;Volume: 20 Issue: 7 Pages: 491-503 Article Number: PII 907419577
Type:Article
Keywords:University for Laguerre and Hermite polynomials
,
spectral methods
,
expansion coefficients
Abstract:
Two new formulae expressing explicitly the integrals of Laguerre (Hermite) polynomials of any degree and for any order in terms of the Laguerre (Hermite) polynomials themselves are proved. Another two new explicit formulae relating the Laguerre (Hermite) coefficients of an expansion for an infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function are also established. An application of these formulae for solving ordinary differential equations with varying coefficients is discussed.