- #1
RJLiberator
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Homework Statement
Complex Analysis Problem:
The euler Numbers E_n, n=0, 1, 2,..., are defined by 1/cosh(z) = the sum from n=0 to n=infinity of E_n/n! z^n (|z|<pi/2).
show that E_n=0 for n odd. Calculus E_0, E_2, E_4, E_6
Homework Equations
Not entirely sure what to put here for this one.
The Attempt at a Solution
I've been stuck on this one for a little while now.
I started out by just writing out the terms.
E_0+E_1*z+E_2/2! z^2+...
I know that the coshz is an even function, I know the first x amount of terms of Euler's Numbers, but I'm struggling on how to 'prove' that Odd Euler Numbers are = 0.
Any guidance on getting me going here?
Thank you kindly.