Show that {\/? sin(n – )(4)} is an orthonormal set in C(0,1). State condition(s) under which an arbitrary f E C(0,1) can be expanded as a series wrt the orthonormal set above. Assume that the above condition(s) is satisfied, find the expansion of the function f(x) = 1 on [0, 1] with respect to the orthonormal set above.
Show that {\/? sin(n – )(4)} is an orthonormal set in C(0,1). State condition(s) under which an arbitrary f E C(0,1) can be expanded as a series wrt the orthonormal set above. Assume that the above condition(s) is satisfied, find the expansion of the function f(x) = 1 on [0, 1] with respect to the orthonormal set above.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Part1
![1. Show that {? sin(n – )()} is an orthonormal set in C(0,1).
2. State condition(s) under which an arbitrary f e C(0,1) can be expanded as a series
wrt the orthonormal set above.
3. Assume that the above condition(s) is satisfied, find the expansion of the function
f (x) = 1 on [0, 1] with respect to the orthonormal set above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc6748d3-4cd8-403e-abcc-dc83fd70c599%2F50cb0ed0-4a5c-41b1-aaa1-de7791112a2a%2F1tyojq8_processed.png&w=3840&q=75)
Transcribed Image Text:1. Show that {? sin(n – )()} is an orthonormal set in C(0,1).
2. State condition(s) under which an arbitrary f e C(0,1) can be expanded as a series
wrt the orthonormal set above.
3. Assume that the above condition(s) is satisfied, find the expansion of the function
f (x) = 1 on [0, 1] with respect to the orthonormal set above.
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