Suppose that g is holomorphic on C, and satisfies g(z)| ≤|z¹/2 for all z € C\ {0} (where 2/¹/2 is the usual positive real square root). Prove that g is constant. (Hint: consider the Taylor series expansion centred at 0.) 1120) (7.70) ³. as 20=0

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
(b) Suppose that g is holomorphic on C, and satisfies g(z)| ≤|z¹/2 for all z € C\ {0} (where
21/2 is the usual positive real square root). Prove that g is constant. (Hint: consider the
Taylor series expansion centred at 0.)
€2120) (7-20) J.
as Zo=0
Transcribed Image Text:(b) Suppose that g is holomorphic on C, and satisfies g(z)| ≤|z¹/2 for all z € C\ {0} (where 21/2 is the usual positive real square root). Prove that g is constant. (Hint: consider the Taylor series expansion centred at 0.) €2120) (7-20) J. as Zo=0
Expert Solution
steps

Step by step

Solved in 3 steps with 2 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,