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 .
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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