A simple proof of Lerch´s formula
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 .
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Two Fractional part Integrals related to ln (Γ(z))
In this post we will present proofs for the follwoing two integrals related to the LoGamma function: Click here to see it.
POISSON SUMMATION COSH SUM
We want to prove the following transformation formula that appears in this twitter post Click here to see the proof . We used the result proved here .
INTEGRALBOT BETA-DIGAMMA INTEGRAL
Today we will show the following result that appears in this twitter post We will start by proving two lemmas involving the Beta and Digamma functions. Lemma 1: (1) Recall the Beta function (2) If we differentiate (2) w.r. to s we obtain Lemma 2: (3) Recall the Beta function (4) If we differentiate (4) w.r. to a we obtain Now let´s evaluate the integral: For the proof of the special values of the Digamma function see this post . Plugging the values of J and K back in the original integral we obtain: