An alternate infinite series involving sinh(n \pi)
In this entry we present a proof via contour integration for the following alternate infinite series Click here for the proof.
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Two remarkable sums due to Ramanujan-Part II
In this entry we present a second proof via contour integration for the series (proved previously here ) Click here for the proof.
Two remarkable sums due to Ramanujan-Part I
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.
Another quick contour integral from the integralbot
In this blog entry we solve another integral from @integralbot via contour integration. Click here for the proof.
Transformation formula Dedekind´s eta function
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.
A Ramanujan Series
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
Integral of an infinite product
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 .