If f is holomorphic | f(n) (0)| n! |an| = on D(0, 1) and [ƒ(2)| < 1, show that ≤ (n + 1) [ 1 + (₁ ²) " ≤ e(n+1). Use a Cauchy estimate with integration on C(0,r) and choose r = n n+1•

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
100%
If f is holomorphic on D(0, 1) and [ƒ(2)| < show that
| f(n)
|ax| = 10) (0)| ≤ (x + 1) (1+1)
(n
n!
n
≤ e(n + 1).
Hint: Use a Cauchy estimate with integration on C(0,r) and choose r =
n
n+1°
Transcribed Image Text:If f is holomorphic on D(0, 1) and [ƒ(2)| < show that | f(n) |ax| = 10) (0)| ≤ (x + 1) (1+1) (n n! n ≤ e(n + 1). Hint: Use a Cauchy estimate with integration on C(0,r) and choose r = n n+1°
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,