MY MATEX NOTES

In this post we will show that For , where and . As a Corollary we also obtain the beatiful pair of integrals Click here for the proof.

    Today we will prove the famous Gauss digamma theorem, namely The proof is based on Jensen´s famous proof. Click here for the proof .

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 article we want to prove the following three infinte series: click here for the proof.

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 will prove the following three beautifull infinte series Click here for the proof.

In this entry we present a proof via contour integration for the following alternate infinite series Click here for the proof.

In this entry we present a second proof via contour integration for the series (proved previously here ) Click here for the proof.

In this article we prove two remarkable results due to Ramanujan, namely and To this end we rely on the functional equation that the Dedekind´s eta function obeys, previously proved ( here ): Click here for the proof.

In this blog entry we solve another integral from @integralbot via contour integration. 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 article we prove the following Ramanujan series To this end we will rely on the residues theorem.  Click here  for the proof of the Ramanujan´s series

In this article our goal it to prove the following integral To this end we will rely on two results: Euler´s pentagonal theorem which states that we have proved this before ( see here ). The second tool that we will use regards the evaluation of alternating infinite series using the residues theorem to evaluate the following infinite series Click here for the proof .

In today´s post we will prove the following result by contour integration Click here to read the post.

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.

In this blog entry we will prove Ramanujan´s Psi Sum, namely Click here for the proof. As corollaries of the above formula we show that wich relies also on Jacobi triple product proved here :

In this post we will prove the following result Click here for the proof We have relied on the previous established result Proof   here .

In this entry we will solve the following integral to this end we should recall a previous established result. Click here for the proof of the integral.                       Proof of the binomial series here   .