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Re: Re: Hypergeometric2F1


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
>>
>>
>>
>>



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