On Fri, May 31, 2024 at 06:52:11PM +0200, Grégory Vanuxem wrote:
> Hello,
>
> First there is a small typo in FSFUN:
>
> dilog: dilog(z) is the dilogaritm;
> A missing 'h'.
>
> But I do not understand what this function computes in FriCAS, usually
> it is a special case of polylogarithm of order 2.
We have definition in LiouvillianFunctionCategory:
dilog : % -> %
++ dilog(x) returns the dilogarithm of x, i.e.
++ the integral of \spad{log(x) / (1 - x) dx}.
It is releated to 'polylog(2, x)':
(13) -> polylog(2, x)
(13) dilog(- x + 1)
Type: Expression(Integer)
>
> In SAGE via https://sagecell.sagemath.org/
> dilog(0.7) => 0.889377624286039
(14) -> dilog(0.3)
(14) 0.8893776242_8603873859_98408
Type: Complex(Float)
> WolframAlpha also (https://www.wolframalpha.com/input?i=dilog%5B0.7%5D)
OK. We inherited this definition from original Axiom sources.
And I did literature research and our definition agrees with
what I found in research papers about dilogarithm and
polylogaritms.
It is tempting to change definition, but given usage in math
litarature and our previous use I kept what we had.
> >From https://en.wikipedia.org/wiki/Polylogarithm, there is a
> disambiguation note with lix) (logarithmic integral)
'li(x)' is logarithmic integral, quite a different thing than
dilogarithm. Some folks use 'Li' as name of polylogarthim,
that could be confusing.
> and it seems the
> code use it, but I still don't understand this result in FriCAS:
>
> (3) -> dilog(0.7)
>
> (3) 0.3261295100_7547606953_084133
> Type: Complex(Float)
>
> - Greg
>
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