MY MATEX NOTES

In this post we prove the following infinite sum Click here for the proof. We relied in a few previous established results: Proved here Both proved here . And Proved here .

In this blog entry we will prove the following three results related to the Jacobi Theta function Click here for the proof. It relies on the Jacobi triple product (proved here ) And special value of Jacobi theta function (proved here )

This is a short article to prove the following result To this end we will rely on some previous established results, namely: proved here, and proved here . As a corollary of our goal series we also obtain this nice series Click here  for the proof of our main series.

In this entry we will evaluate symmetric infinite sums of the type To this end we will rely on the previous established result ( proved here ) Click here for the proof.

In this blog entry we prove the transformation formula for the Dedekind´s eta function The proof is due to C.L. Siegel, and it´s done by contour integration. Click here to read it.

In this entry we introduce the Arithmetic Geometric mean and show it´s connection with the complete elliptic integral of the first kind. This relation is one way to establish the connection between the Jacobi theta function and elliptic integral. and Click here to read the article. Important to note that in this entry we wont get into a detailed study of elliptic integral. Commentaries and feedbacks are welcome.

This entry has some of the infinite product related to Jacobi Theta function proved. Click here to read it. The Jacobi triple product proved here , plays a central role in their proof as well some special values of the Jacobi theta function, see here