Re: Re: Hypergeometric2F1

• To: mathgroup at smc.vnet.net
• Subject: [mg93227] Re: [mg93183] Re: Hypergeometric2F1
• From: Artur <grafix at csl.pl>
• Date: Fri, 31 Oct 2008 03:09:18 -0500 (EST)
• References: <200810300702.CAA00649@smc.vnet.net>

```Result is correct

Hypergeometric2F1[a,b,c,0]=1

You can understand this when you plot

Plot[{Hypergeometric2F1[1/2,1/3,1/4,x],Hypergeometric2F1[1/5,1/3,1/4,x],
Hypergeometric2F1[1/2,1/3,1/5,x]},{x,-1,1}]

Best wishes
Artur

Bill Rowe pisze:
> On 10/29/08 at 5:50 AM, DWCantrell at sigmaxi.net (David W. Cantrell)
> wrote:
>
>
>> Artur <grafix at csl.pl> 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}
>>>
>
>
>> It seems that you are wanting to determine a,b,c such that
>>
>
>
>> ArcCosh[2]/ArcCosh[2-x]==Hypergeometric2F1[a,b,c,x]
>>
>
>
>> would be an identity for x < 1. But that is not possible. What made
>> you think it would be possible?
>>
>
> Given
>
> In[17]:= Hypergeometric2F1[a, b, c, 0]
>
> Out[17]= 1
>
> It appears there are infinitely many solutions. Is the result
> returned by Mathematica for Hypergeometric2F1[a,b,c,x] incorrect
> when x = 0? What am I missing here?
>
>
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```

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