Re: What inspite FindInstance ?
- To: mathgroup at smc.vnet.net
- Subject: [mg108001] Re: [mg107955] What inspite FindInstance ?
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Fri, 5 Mar 2010 04:30:50 -0500 (EST)
- References: <201003041025.FAA26461@smc.vnet.net>
Artur wrote:
> Dear Mathematica Gurus,
>
> Mathematical problem is following:
> Find rational numbers a,b,c such that
> (Pi^2)*a+b+c*Catalan==Zeta[2,5/k] for some k
> e.g.
> FindInstance[
> Zeta[2, 5/4] -a Pi^2 - b - c Catalan == 0, {a, b, c}, Rationals]
> give answer
> FindInstance::nsmet: The methods available to FindInstance are
> insufficient to find the requested instances or prove they do not exist. >>
>
>
> What inspite FindInstance? (I know that we can do 6 loops (3
> Denominators and 3 Numerators) but we have to have luck to give good
> range of loops..
>
> Good answer for my example is {a,b,c}={1,-16,8}but in general case these
> a,b,c will be rationals (not integers)
> e.g. (Pi^2)*a+b+c*Catalan==Zeta[2,5/2] we have {a,b,c}={1/2,-40/9,0}
> but this last case Mathematica deduced autmathically if we execute :
> Zeta[2,5/2]
> first one none.
>
> Best wishes
> Artur
Here is an approach that involves much less code than what I last sent
(in the tehcnical sense that "none" is much less than "some").
(1) Go to
http://www.wolframalpha.com
(2) Enter
zeta(2,5/2)
or
zeta(2,5/4)
Results for teh first include a pane
Exact result:
pi^2/2-40/9
Results for the second have a pane
Alternate form:
8 C-16+pi^2
That Wolfram|Alpha is one clever gal.
Daniel Lichtblau
Wolfram Research
- References:
- What inspite FindInstance ?
- From: Artur <grafix@csl.pl>
- What inspite FindInstance ?