The period of summation functions

Luongo
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1. how do i find the period of summation of some function ie: 2^-k or cos(pi k) multiplied by some complex exponential ei7kt

ie: f( t ) = \sum 2-kei7kt
2. does anyone know the formula for finding the period of summations of complex exponentials? note this is for fourier
3. would i say that omega is 7k by Euler's method. if i converted to sines and cosines, thus the period T = 2pi/7?
is this how i would find the period of this summation?
 
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The definition of periodicity is as follows:
If T is the period of a function f(t) then,
f(t+ T) = f(t).

Does your answer admit to this definition ?
 
╔(σ_σ)╝ said:
The definition of periodicity is as follows:
If T is the period of a function f(t) then,
f(t+ T) = f(t).

Does your answer admit to this definition ?

i think so thanks
 
You are welcome. :-)
 
╔(σ_σ)╝ said:
You are welcome. :-)


my friend said i am wrong...?
 
Luongo said:
my friend said i am wrong...?
What is his reasoning ?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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