Howtosignalprocessing
- What is the integration of 1 z?
- Does 1 z have a primitive?
- What is the integration of Cos z?
- How do you use Cauchy integral formula?
What is the integration of 1 z?
The only singularity of the function f(z) = 1/z is at z=0 and so the (line) integral of 1/z around any closed contour not enclosing z=0, is 0.
Does 1 z have a primitive?
From our experience with one variable calculus, ∫ 1/x dx = log x, so a natural primitive for 1/z would be log z. In fact by the chain rule, if we want to define the logarithm as the inverse function to the exponential, the derivative will have to be 1/z.
What is the integration of Cos z?
Book gives ∮Cos(z)(z−a)mdz=∞∑k=0∮ak(z−a)kk! (z−a)mdz=2πiam−1(m−1)!
How do you use Cauchy integral formula?
Statement: If f(z) is an analytic function in a simply-connected region R, then ∫c f(z) dz = 0 for every closed contour c contained in R. If f(z) is an analytic function and its derivative f'(z) is continuous at all points within and on a simple closed curve C, then ∫c f(z) dz = 0.
