Picard's Little Theorem and Twice-Punctured Plane
We show that the range of a non-constant entire function's range cannot be a twice-punctured plane.
Picard's Little Theorem and Twice-Punctured Plane
A Step-by-step of the Analytic Continuation of the Riemann Zeta Function
We compute the analytic continuation of the Riemann Zeta function and after that the reader will realise that asserting $1+2+\dots=-\frac{1}{12}$ without enough caution is not a good idea.
A Step-by-step of the Analytic Continuation of the Riemann Zeta Function
A Detailed Proof of the Riemann Mapping Theorem
We offer a detailed proof of the Riemann mapping theorem, which states that every proper simply connected region is conformally equivalent to the open unit disc.
A Detailed Proof of the Riemann Mapping Theorem
Quasi-analytic Classes
We study the concept of quasi-analytic functions, which are quite close to being analytic.
Quasi-analytic Classes
The Fourier transform of sinx/x and (sinx/x)^2 and more
In this post we compute the Fourier transform of $\sin{x}/x$ and $(\sin{x}/x)^2$ through contour integration.
The Fourier transform of sinx/x and (sinx/x)^2 and more