Problem 3. Let fn(x) = x^ (ln(x) – Hn). fn+1(2) [ fn(x) dx = Show that n+1 Remark: Note that fo(x) = ln(x), so the functions fn(x) are "higher order antiderivatives" of ln(x). + C.
Problem 3. Let fn(x) = x^ (ln(x) – Hn). fn+1(2) [ fn(x) dx = Show that n+1 Remark: Note that fo(x) = ln(x), so the functions fn(x) are "higher order antiderivatives" of ln(x). + C.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Problem 3. Let
fn(x)=x" (ln(x) - Hn).
fn+1(2)
n+1
[ fn(x) dx =
Show that
Remark: Note that fo(x) = ln(x), so the functions fn(x) are "higher order antiderivatives" of In(x).
+ C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf18211f-0280-4890-b969-3ee778ce7d32%2Fa2e94bea-fb2a-42ff-87c9-8fe13738f566%2Fes60xbb_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 3. Let
fn(x)=x" (ln(x) - Hn).
fn+1(2)
n+1
[ fn(x) dx =
Show that
Remark: Note that fo(x) = ln(x), so the functions fn(x) are "higher order antiderivatives" of In(x).
+ C.
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