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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 16, Problem 20PS

Textbook Problem

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**Laguerre’s Equation** Consider **Laguerre’s Equation**

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

to show that

Assume that

Determine the Laguerre polynomials

**(a)**

To determine

**To prove:** The Laguerre’spolynomial is given by

**Given information:**

The given Laguerre’s 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,

Inserting the values of

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

**(b)**

To determine

The values of Laguerre’s polynomials

Multivariable Calculus

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Finding a General Solution Find the general...Ch. 16 - Distinct Real Zeros Given that the characteristic...Ch. 16 - Limit of a Solution Given that a and b are...Ch. 16 - Trivial and Nontrivial Solutions Consider the...Ch. 16 - Eulers Differential Equation Eulers differential...Ch. 16 - Pendulum Consider a pendulum of length L that...Ch. 16 - Deflection of a Beam A horizontal beam with a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Airys Equation Consider Airys equation given in...Ch. 16 - ChebyshevsEquation ConsiderChebyshevs equation...Ch. 16 - Bessels Equation: Order Zero The differential...Ch. 16 - Bessels Equation: Order One The differential...Ch. 16 - Hermites Equation Consider Hermites Equation...Ch. 16 - Laguerres Equation Consider Laguerres Equation...

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