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MY MATEX NOTES

This is a collection of personal notes from a non mathematician with techniques that I have learned throughout the years focused mostly in integrals. It´s mainly goal is to organize my manuscripts in a more cleaner and readable format and share with whoever finds it interesting.

Another quick contour integral from the integralbot

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December 27, 2022

In this blog entry we solve another integral from @integralbot via contour integration.

$\begin{align*} \int_0^\infty \frac{e^{\cos ax}\cos\left(\sin ax+bx \right)}{c^2+x^2}\,dx&=\frac{\pi}{2c}e^{e^{-ac}-bc} \end{align*}$

Click here for the proof.

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Ramanujan´s Psi Sum

September 29, 2022

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 :

Infinite sum reciprocal hyperbolic sine squared

January 18, 2023

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.

LAPLACE TRANSFORM OF A COMPLEX POWER

August 17, 2023

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.

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