LAPLACE TRANSFORM OF A COMPLEX POWER
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.
Posts
GAUSS DIGAMMA THEOREM
Today we will prove the famous Gauss digamma theorem, namely The proof is based on Jensen´s famous proof. Click here for the proof .
Infinite series involving sech squared PART II
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 .
INFINITE SERIES INVOLVING \sech^2(n \pi s)
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 )
Infinite sum reciprocal hyperbolic sine squared
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.
Infinite series involving hyperbolic cotangent
In this article we want to prove the following three infinte series: click here for the proof.
Lattice sums
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.
Summing some Eisenstein series
In this blog entry we will prove the following three beautifull infinte series Click here for the proof.