# Hermite’s Equation Consider Hermite’s Equation y ' ' − 2 x y ' + 2 k y = 0 Use a power series of the form y = ∑ n = 0 ∞ a n ( x ) n to find the solution when k = 4 . [Hint: Choose the arbitrary constants such that the leading term is ( 2 x ) k .] Polynomial solutions of Hermite’s equation are called Hermite polynomials and are denoted by H k ( x ) . The general form of H k ( x ) can be written as H k ( x ) = ∑ n = 0 P ( − 1 ) n k ! ( 2 x ) k − 2 n n ! ( k − 2 n ) !

### 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 19PS
Textbook Problem

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