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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 16, Problem 19PS

Textbook Problem

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**Hermite’s Equation** Consider **Hermite’s Equation**

Use a power series of the form

to find the solution when

Polynomial solutions of Hermite’s equation are called Hermite polynomials and are denoted by

**(a)**

To determine

**To calculate:** The solution of the Hermite’s equation,

**Given information:**

The given differential equation is

**Concept Used:**

Power series is defined as an infinite series of the form,

**Calculation:**

Assume

Again differentiating above equation with respect to

Now, the given differential equation is,

For obtaining the solution when

Insert the values of

Equating the coefficients of like terms, one can obtain the recursion formula

**(b)**

To determine

The values of Hermite polynomials

Multivariable Calculus

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