- #1

- 20

- 0

## Main Question or Discussion Point

How to show that if f is an entire function,such that f(z) = f(z + 2π ) and f(z) = f(z + 2π i)

for all z belong to C.

π is pi.

for all z belong to C.

π is pi.

- Thread starter alvielwj
- Start date

- #1

- 20

- 0

How to show that if f is an entire function,such that f(z) = f(z + 2π ) and f(z) = f(z + 2π i)

for all z belong to C.

π is pi.

for all z belong to C.

π is pi.

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 956

How to show "if ...."How to show that if f is an entire function,such that f(z) = f(z + 2π ) and f(z) = f(z + 2π i)

for all z belong to C.

π is pi.

but where is your conclusion? What do you want to prove?

- #3

- 20

- 0

first show f is bounded,then by the Liouville's theorem, f is constant

- #4

- 20

- 0

Suppose that f is an entire function such that f(z) = f(z + 2π ) and f(z) = f(z + 2π i)

for all z belong to C. Use Liouville's theorem to show that f is constant.

Hint: Consider the restriction of f to the square {z = x + iy : 0 <x < 2π ; 0 < y <2π }

- #5

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 956

- #6

- 20

- 0

I finally know how to use the hint..

At the begining i really dont know how to start..

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 4

- Views
- 772

- Replies
- 4

- Views
- 8K

- Last Post

- Replies
- 4

- Views
- 690

- Last Post

- Replies
- 9

- Views
- 2K

- Last Post

- Replies
- 6

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 919

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 6

- Views
- 1K