Determine whether the system is linear

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and how make check the linearity and shift invarient for the system

I want to determine whether the system is linear and shift invarientby steps

g(m,n) = f(m,-1) + f(m,0) + f(m,1)

g(x) = (integration from +infinety to - infinety) f(x,z) dz

please help me
Thanks alot
 
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hanafnaf said:
and how make check the linearity and shift invarient for the system

I want to determine whether the system is linear and shift invarientby steps

g(m,n) = f(m,-1) + f(m,0) + f(m,1)

g(x) = (integration from +infinety to - infinety) f(x,z) dz

please help me
Thanks alot

What can you tell us about how to test for linearity?
 

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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