A log trig integral \int_0^{\pi/2}\ln\left(1+a\sin^2 x \right) \,dx
In this post we will prove the following result Click here for the proof We have relied on the previous established result Proof here .
Posts
Trig integral equals alternate inverse reciprocal binomial series
In this entry we will solve the following integral to this end we should recall a previous established result. Click here for the proof of the integral. Proof of the binomial series here .
log log integral inverse sech
In this entry we will prove the following result Click here to read it. Some previous established results were used, i.e.: Lerch´s formula Click here for the proof. Relation between Bernoulli´s polynomials and Hurwitz zeta function click here for the proof (equations 8.22 and 8.30)
INFINITE PRODUCTS AND JACOBI THETA FUNCTION
This entry has some of the infinite product related to Jacobi Theta function proved. Click here to read it. The Jacobi triple product proved here , plays a central role in their proof as well some special values of the Jacobi theta function, see here
Series involving reciprocal of the central binomial coefficient squared
Today we will prove this infinite series which involves the reciprocal of the central binomial coefficient squared, namely Click here for the proof.
Central Binomial representation for zeta(2)
In this post we will prove the following nice series representation for : Click here for the proof. We used the previous established result Click here for the proof.
Central Binomial coefficient series and Catalan Constant
In this blog entry we will prove the following result: Click here for the proof.