Let ##\gamma## be a closed curve in ##\mathbb{C}##. If ##\gamma## doesn't contain any point from [2,5] in its interior, then ##\int_{\gamma}f=0## since f is holomorphic away from [2,5]. Suppose that ##\gamma## contains [2,5] in its interior. Let R be a rectangle oriented with the coordinate...
For your solution when k=1, why do you have [-1,\infty)?
If t = -1, you are dividing by zero.
What is wrong with the (-\infty, -1)?
(-2)^2-4+1>0 Is this true for the entire set?
I have this proof for finite points but how would I modify it for infinite many points between [2,5]?
Assume q(z) is any function that is holomorphic on a disc U except at a finite number of points \xi_1,\ldots, \xi_n\in U, and assume \lim_{z\to\xi_j}(z-\xi_j)q(z)=0 for 1\leq j\leq n. Let...
So I am trying to use Morera's Theorem:
Let U be an open set in C and let f be continuous on U. Assume that the integral of f along the boundary of every closed rectangle in U is 0. Then f is holomorphic.
So let U = \mathbb{C} - [2,5] Let R be rectangles in U which are parallel to the...
If you set I = integral and multiplied by the same integral, you would have I^2. When you solve that you get 2pi but then you take the square root.
However, isn't is supposed to be equal to \frac{1}{\sqrt{2\pi}