05/05/2014, 06:18 PM

OMG. FOund a very nice theorem in complex analysis. I found it referenced in this paper.

http://algo.inria.fr/seminars/sem01-02/delabaere2.pdf

[4] Boas, Jr. (Ralph Philip). – Entire functions. – Academic Press, New York, 1954, x+276p.

It says that:

"In fact, if a and b are two [holomorphic] functions that are of exponential type α < π, if a(n) = b(n) for all

n ≥ 1, then a = b, due to a theorem by Carlson [4]."

THEREfore if:

for and

We know implies !!!!!

This is a nice uniqueness result.

http://algo.inria.fr/seminars/sem01-02/delabaere2.pdf

[4] Boas, Jr. (Ralph Philip). – Entire functions. – Academic Press, New York, 1954, x+276p.

It says that:

"In fact, if a and b are two [holomorphic] functions that are of exponential type α < π, if a(n) = b(n) for all

n ≥ 1, then a = b, due to a theorem by Carlson [4]."

THEREfore if:

for and

We know implies !!!!!

This is a nice uniqueness result.