You are Here: Home >< Maths

complex analysis watch

1. question on uniqueness theorem:

let f be an entire function s.t

f(i/n)=cos(1/n) for n a positive integer

show f(z)=cosh (z)

done this by considering S={i/n for n positive integer} noting both f and cosh agree on S and S has limit point.

the next part is

ii) find an entire function f other than f(z)=cosh(z)) that satisfies

f(in)=cos n for n a positive integer

can I just put something like

f(z)=sin(2(pi)z/i) + cos (z/i)? is there any deep justification for any function apart from cosh(z)?

can someone explain how the uniqueness theorem fails on part(ii)

thanks
2. (Original post by mathz)
question on uniqueness theorem:

let f be an entire function s.t

f(i/n)=cos(1/n) for n a positive integer

show f(z)=cosh (z)

done this by considering S={i/n for n positive integer} noting both f and cosh agree on S and S has limit point.

the next part is

ii) find an entire function f other than f(z)=cosh(z)) that satisfies

f(in)=cos n for n a positive integer

can I just put something like

f(z)=sin(2(pi)z/i) + cos (z/i)? is there any deep justification for any function apart from cosh(z)?

can someone explain how the uniqueness theorem fails on part(ii)

thanks

The uniqueness theorem doesn't apply as the points don't have a limit point in this case.

Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 3, 2017
Today on TSR

Edexcel C2 Core Unofficial Markscheme!

Find out how you've done here

Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE