Consider the Laguerre differential equation x2y′′+x(1−x)y′+Nxy=0, (11.5.40) where N is a constant. Show that in the case when N is a positive integer, Equation (11.5.40) has a solution that is a polynomial of degree N, and find it. When properly normalized, these solutions are called the Laguerre polynomials.
Consider the Laguerre differential equation x2y′′+x(1−x)y′+Nxy=0, (11.5.40) where N is a constant. Show that in the case when N is a positive integer, Equation (11.5.40) has a solution that is a polynomial of degree N, and find it. When properly normalized, these solutions are called the Laguerre polynomials.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 10CR
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Consider the Laguerre differential equation x2y′′+x(1−x)y′+Nxy=0, (11.5.40) where N is a constant. Show that in the case when N is a positive integer, Equation (11.5.40) has a solution that is a polynomial of degree N, and find it. When properly normalized, these solutions are called the Laguerre polynomials.
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