# Laguerre’s Equation Consider Laguerre’s Equation x y ' ' + ( 1 − x ) y ' + k y = 0 . Polynomial solutions of Laguerre’s equation are called Laguerre polynomials and are denoted by L k ( x ) . Use a power series of the form y = ∑ n = 0 ∞ a n x n to show that L k ( x ) = ∑ n = 0 k ( − 1 ) n k ! x n ( k − n ) ! ( n ! ) 2 Assume that a 0 = 1 . Determine the Laguerre polynomials L 0 ( x ) , L 1 ( x ) , L 2 ( x ) , L 3 ( x ) , and L 4 ( x ) . ### Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378 ### Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378

#### Solutions

Chapter 16, Problem 20PS
Textbook Problem

## Expert Solution

### Want to see the full answer?

Check out a sample textbook solution.

### Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times vary by subject and question complexity. Median response time is 34 minutes and may be longer for new subjects. 