Re: Re: Hypergeometric2F1

• To: mathgroup at smc.vnet.net
• Subject: [mg93266] Re: [mg93156] Re: [mg93136] Hypergeometric2F1
• From: Artur <grafix at csl.pl>
• Date: Sat, 1 Nov 2008 05:12:26 -0500 (EST)
• References: <200810280954.EAA22098@smc.vnet.net> <200810291049.FAA09463@smc.vnet.net>

```I'm agree that my previous sample wasn't good ArcCosh[2]/ArcCosh[2-x]
with FindInstance (I was think about FindFit (interpolating).
The best interpolation known for me is:
Plot[{ArcCosh[2]/ArcCosh[2 - x], Hypergeometric2F1[1/2, 2/3, 4/5, x]},
{x, -4, 1}]
I'm looking for better

I'm still looking for working procedure procedure for:
FindInstance[Hypergeometric2F1[1/3, a/3, 5/6, b/32] == 8/5, {a, b}]
what inspite FindInstance ?

or

FindInstance[2 Cos[2 Pi x] == Hypergeometric2F1[1/2 + a x, 1/2 + b x,
1/2, 3/4] ,{a,b}]

As I was informed earlier procedure of Andrzej Kozlowski don't work with
Hypergeometric2F1
e.g.
In[1]: FindInstance[ LogicalExpand[
2 Cos[2 Pi x] - Hypergeometric2F1[1/2 + a x, 1/2 + b x, 1/2, 3/4] +
O[x]^5 == 0], {a, b}]
Out[1]:{}

True answer is {a,b}={-3,3} or {a,b}={3,-3}

Because always Andrzej Kozlowski's procedure return {} if is used with
Hypergeometric2F1 we can also prooved with use of them Fermat Last Theory.

Between beliving that procedure work and true working is infinity.

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
>
>
>
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>
> The message was checked by ESET NOD32 Antivirus.
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```

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