Let f(x) be defined for all rational number a in the interval [0, 1]. Let F(x) and F;(x) be defined by
Let f(x) be defined for all rational number a in the interval [0, 1]. Let F(x) and F;(x) be defined by
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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Question
21
![21. Let f(x) be defined for all rational number a in the interval [0, 1]. Let F(x) and F1(x)
be defined by
F(n) = E.
F (n) = E f
and
k=1
k=1
(k, n)=1
Prove that
(i) F1 = F * µ.
(ii) Using (i) (or some other way) prove that
where e(x)
e2mir
e
k=1
(k, n)=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14ecf344-ce8f-4775-bc92-58dda47891ff%2F5848c3c0-9fb7-473f-97f4-5adc670a2915%2Fl7859ts_processed.jpeg&w=3840&q=75)
Transcribed Image Text:21. Let f(x) be defined for all rational number a in the interval [0, 1]. Let F(x) and F1(x)
be defined by
F(n) = E.
F (n) = E f
and
k=1
k=1
(k, n)=1
Prove that
(i) F1 = F * µ.
(ii) Using (i) (or some other way) prove that
where e(x)
e2mir
e
k=1
(k, n)=1
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