The World Renowned Nose Pdf 16

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The World Renowned Nose Pdf 16

 

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The World Renowned Nose PDF 16

The World Renowned Nose PDF 16, The World Renowned Nose PDF 16 History and Linguistics. the world renowned nose pdf 16. the world renowned nose pdf 16. World Renowned Nose PDF16. 0.0.0.0 from 107.0 MB.Q:

An integral involving Struve functions

How can I compute this integral?
$$ I=\int_0^\infty\,\mathrm{Li}_3(-e^{ -x})\,dx$$

A:

Here is a nice reference.
Somehow one can find $\mathrm{Li}_3$ and $\log$ by hand, but it is harder than it looks.

Generalizations of the Liouville function $\mathrm{Li}_3(x)$ can be found by computer search. They are related to the coefficients of
$$ \sum_{k=1}^\infty \frac{\mathrm{Li}_3(x^k)}{k!} (-1)^k
$$
in some parameterization of the elliptic integrals.

Note: The same is true of your integral.

A:

I have no idea about the integral $\displaystyle I=\int_0^\infty\,\mathrm{Li}_3(-e^{ -x})\,dx$
If one want to solve the case $\displaystyle \int_0^\infty\,\mathrm{Li}_3(-e^{ -x})e^{ -x}dx$ using the power series expansion of $\mathrm{Li}_3(-e^{ -x})$, one can
\begin{align}
\mathrm{Li}_3(-e^{ -x})e^{ -x}
& = -3(e^x+x)-2(e^x+x)^2+\ https://fennylaw.com/wp-content/uploads/2022/06/sallaur.pdf

 

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