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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.4: Logarithmic Functions

Problem 46E

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Number theory question

define A(x) by
A(x) = Σa(n),
n<x
a: 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
Σ a(n)f(n) = A(z)f(x) — A(y)f(y) — ["* A(t)ƒ'(t)}dt
Y
y<n<x
P.1)

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