Concept explainers
(a) Laguerre’s differential equation
is known to possess polynomial solutions when n is a nonnegative integer. These solutions are naturally called Laguerre polynomials and are denoted by Ln(t). Find
(b) Show that
where
This last relation for generating the Laguerre polynomials is the analogue of Rodrigues’ formula for the Legendre polynomials. See (36) in Section 6.4.
Rodrigues’ formula for these polynomials is
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First Course in Differential Equations (Instructor's)
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,