       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/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*ArcCosh) +
4/(27*ArcCosh^2) + 1/(3*Sqrt*ArcCosh^3) +
1/(9*ArcCosh^4) == 0 &&
-((a*(a + 1)*(a + 2)*b*(b + 1)*(b + 2))/
(6*c*(c + 1)*(c + 2))) +
1/(6*Sqrt*ArcCosh) + 2/(9*ArcCosh^2) +
1/(3*Sqrt*ArcCosh^3) == 0 &&
-((a*(a + 1)*b*(b + 1))/(2*c*(c + 1))) +
1/(3*Sqrt*ArcCosh) + 1/(3*ArcCosh^2) ==
0 && 1/(Sqrt*ArcCosh) - (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: 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:{0.297, FindInstance[9/5 - Hypergeometric2F1[1/4, 1/2, c,
> 80/81] == 0,
>  c]}
>
>
> Because FindInstance crash on one parameter equation from these
> reason we can be 100% sure that also crash on 3 parameters equation.
>
> 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/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/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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