We present a systematic study of integrals over [0,1] where the integrand is of the form Q(x) log log 1/x. Here Q is a rational function.
Part 1. Infinite series and logarithmic integrals associated to differentiation with respect to parameters of the Whittaker $\mathrm{M}_{κ,μ}\left( x\right) $ function
Part 2. Infinite series and logarithmic integrals associated to differentiation with respect to parameters of the Whittaker $\mathrm{W}_{κ,μ}\left( x\right) $ function
The integrals in Gradshteyn and Rhyzik. Part 1: A family of logarithmic integrals
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