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!
Asked
Active
Viewed 427 times
6
-
2https://arxiv.org/abs/1910.12113 – Infiniticism Jun 03 '20 at 05:10
-
2You might find info here useful. – pisco Feb 03 '21 at 14:48
1 Answers
12
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.
andre
- 1,284