(a) Explanation Given: The equation is f ( x ) = a 0 2 + ∑ n = 1 ∞ ( a n cos n π p x + b n sin n π p x ) , the coefficients are c 0 = a 0 2 , c n = a n − i b n 2 , c − n = a n + i b n 2 and the identities are cos n π p x = e i n π x p + e − i n π x p 2 , sin n π p x = e i n π x p − e − i n π x p 2 . Calculation: The given coefficients are c 0 = a 0 2 , c n = a n − i b n 2 and c − n = a n + i b n 2 . The given equation is f ( x ) = a 0 2 + ∑ n = 1 ∞ ( a n cos n π p x + b n sin n π p x ) (b) To determine To show: The given coefficients can be written in general expression form of integral.

Differential Equations with Boundary-Value Problems

9th Edition

ISBN: 9781337632515

Author: Dennis G. Zill

Publisher: Cengage Learning US

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Question

Chapter 11.2, Problem 23E

(a)

To determine

To show: The given equation can be written in the complex form f(x)=∑n=−∞∞cneinxπp.

(b)

To determine

To show: The given coefficients can be written in general expression form of integral.

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Chapter 11.2, Problem 22E

Chapter 11.2, Problem 24E

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Chapter 11 Solutions

Differential Equations with Boundary-Value Problems

Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - In problem 16 show that the given functions are...Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - In Problems 712 show that the given set of...Ch. 11.1 - In Problems 712 show that the given set of...Ch. 11.1 - In Problems 712 show that the given set of...

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The given equation can be written in the complex form f ( x ) = ∑ n = − ∞ ∞ c n e i n x π p .

Solution Summary: The author explains that the given equation can be written in the complex form f(x)=displaystyle undersetn=-infty

To show: The given equation can be written in the complex form f(x)=∑n=−∞∞cneinxπp.

To show: The given coefficients can be written in general expression form of integral.

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Chapter 11 Solutions