MY MATEX NOTES

In this post we will prove the following integral Click here to see the proof. We will need the following results previously established proved here , and proved here

Today we will prove the following result seen in this Twitter post : First we need a Lemma: Lemma 1: (1) Proof: Corollary: If we let in (1) we obtain (2) Now, consider the following integral (3) Proof: Where in (*) we used the following result proved here Now if we differentiate (3) with respect to s and let we get where we used that (see here ) and

Today we will prove the following result that appears in this Twitter post Click here to see the proof.

In this post we well prove the following results Click here to see the proof.

Today we will prove the following result seen in this post Click here to see the proof

In today´s blog entry we will prove the following infinte sum Click here to see the proof.

In this post we will prove the following result We start by recalling Hermite´s integral representation of the Hurwitz zeta function (proved here ) (1) We may rewrite it in a slightly different way which facilitates some calculations, to this end we start with the following lemma: Lemma: Proof: We can therefore rewrite (1) as (2) Differentiating (2) w.r. to s we obtain (3) Letting and using the logarithmic representation of arctan we obtain rearranging terms we get: Now let to obtain Which concludes the proof. Note: In the proof above we used the following previously established results Proved here Proved here Proved here

In this blog entry we will present a simple proof for Lerch´s formula (1) We rely on the previous established result (see proof here ) Click here to see the proof of   .