This page at I&S forum defines the Generalized Logarithmic Integral as $$L\left[ \begin{matrix} a,b,c \\ d,e,f \end{matrix};z\right] =\int_0^z \frac{\log^a x \log^b(1-x)\log^c(1+x)}{x^d (1-x)^e (1+x)^f} dx.$$ and gives several interesting closed forms for certain combinations of the parameters. I am looking for books, papers or other references where integrals of this form are studied and (at least some of) the closed forms given on that page are proved. Thanks!
2026-03-28 13:50:12.1774705812
Generalized Logarithmic Integral - reference request
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Most of the integrals I have found in my version of Gradshteyn and Rhyzik have as reference [BI], which means
[BI] Bierens de Haan, D., Nouvelles tables d'integrales definies. Amsterdam, 1867.
which can be found here
https://archive.org/details/nouvetaintegral00haanrich
The PDF has 762 scanned pages, which makes it really slow for viewing.
There is also a project, initiated by Victor Hugo Moll, to find proofs for the integrals in Gradshteyn and Rhyzik.
http://www.math.tulane.edu/~vhm/Table.html
there you can look for "logarithm" and click the green links (proofs) if available. I hope this helps.