define A(x) by A(x) = Σ a(n), n≤x .: Let a(n) be an arithmetical function. We where A(x) = 0 if x < 1. Let f has continuous derivative on the interval [y, x], where 0
define A(x) by A(x) = Σ a(n), n≤x .: Let a(n) be an arithmetical function. We where A(x) = 0 if x < 1. Let f has continuous derivative on the interval [y, x], where 0
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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![define A(x) by
A(x) = Σ a(n),
n<x
: Let a(n) be an arithmetical function. We
where A(x) = 0 if x < 1.
Let f has continuous derivative on the interval [y, x], where 0 < y < x. Then we have
Cx
Σ a(n)ƒ(n) = A(x)ƒ(x) — A(y)ƒ(y) — [*ª* A(t)ƒ' (t)}dt
y<n<x
Y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9149ca68-66d8-4eb1-bbfa-98cc7c82f78f%2F698bca0b-2599-4786-b604-9dcd1ba81f62%2Fdoqtkcf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:define A(x) by
A(x) = Σ a(n),
n<x
: Let a(n) be an arithmetical function. We
where A(x) = 0 if x < 1.
Let f has continuous derivative on the interval [y, x], where 0 < y < x. Then we have
Cx
Σ a(n)ƒ(n) = A(x)ƒ(x) — A(y)ƒ(y) — [*ª* A(t)ƒ' (t)}dt
y<n<x
Y
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