Re: Re: Hypergeometric2F1
- To: mathgroup at smc.vnet.net
- Subject: [mg93195] Re: [mg93156] Re: [mg93136] Hypergeometric2F1
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Thu, 30 Oct 2008 02:04:43 -0500 (EST)
- References: <200810280954.EAA22098@smc.vnet.net> <200810291049.FAA09463@smc.vnet.net> <49086272.5090408@csl.pl>
I am amazed that someone would actually write this sort of thing
without bothering to execute the code that was actually posted.
LogicalExpand[ArcCosh[2]/ArcCosh[2 - x] -
Hypergeometric2F1[a, b, c, x] + O[x]^5 == 0]
-((a*(a + 1)*(a + 2)*(a + 3)*b*(b + 1)*(b + 2)*
(b + 3))/(24*c*(c + 1)*(c + 2)*(c + 3))) +
11/(108*Sqrt[3]*ArcCosh[2]) +
4/(27*ArcCosh[2]^2) + 1/(3*Sqrt[3]*ArcCosh[2]^3) +
1/(9*ArcCosh[2]^4) == 0 &&
-((a*(a + 1)*(a + 2)*b*(b + 1)*(b + 2))/
(6*c*(c + 1)*(c + 2))) +
1/(6*Sqrt[3]*ArcCosh[2]) + 2/(9*ArcCosh[2]^2) +
1/(3*Sqrt[3]*ArcCosh[2]^3) == 0 &&
-((a*(a + 1)*b*(b + 1))/(2*c*(c + 1))) +
1/(3*Sqrt[3]*ArcCosh[2]) + 1/(3*ArcCosh[2]^2) ==
0 && 1/(Sqrt[3]*ArcCosh[2]) - (a*b)/c == 0
FindInstance[%, {a, b, c}]
{}
This means that there are no solutions.
FindInstance is certainly an appropriate function to deal with
polynomial equations.
Andrzej Kozlowski
On 29 Oct 2008, at 22:17, Artur wrote:
> Dear Mathematica Gurus!
>
> FindInstance isn't appropriate function to use together with
> Hypergeometric2F1 what we can see on bellow example:
>
> In[1]: FindInstance[9/5 - Hypergeometric2F1[1/4, 1/2, c, 80/81] ==
> 0, c] // Timing
>
> <<FindInstance::nsmet: The methods available to FindInstance are \
> insufficient to find the requested instances or prove they do not \
> exist. >>
>
> Out[1]:{0.297, FindInstance[9/5 - Hypergeometric2F1[1/4, 1/2, c,
> 80/81] == 0,
> c]}
>
> good answer is c=3/4
>
> Because FindInstance crash on one parameter equation from these
> reason we can be 100% sure that also crash on 3 parameters equation.
>
> From these reason I was ask about interpolating function/propcedure
> inspite FindIsntance which will be work with Hypergeometric2F1.
>
>
> Best wishes
> Artur
>
>
>
>
>
> Andrzej Kozlowski pisze:
>> On 28 Oct 2008, at 18:54, Artur wrote:
>>
>>
>>> Dear Mathematica Gurus!
>>> Who know which Mathematica procedure to use to find such a,b,c that
>>> ArcCosh[2]/ArcCosh[2-x]==Hypergeometric2F1[a,b,c,x] for {x,-
>>> Infinity, 1}
>>> BEST WISHES
>>> ARTUR
>>>
>>>
>>
>>
>> What makes you think such a,b,c exist?
>> This seems to indicate that they do not:
>>
>> FindInstance[LogicalExpand[
>> ArcCosh[2]/ArcCosh[2 - x] -
>> Hypergeometric2F1[a, b, c, x] + O[x]^5 ==
>> 0], {a, b, c}]
>> {}
>>
>> Andrzej Kozlowski
>>
>>
>>
>> __________ Information from ESET NOD32 Antivirus, version of virus
>> signature database 3565 (20081029) __________
>>
>> The message was checked by ESET NOD32 Antivirus.
>>
>> http://www.eset.com
>>
>>
>>
>>
- References:
- Hypergeometric2F1
- From: Artur <grafix@csl.pl>
- Re: Hypergeometric2F1
- From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
- Hypergeometric2F1