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Re: Re: Hypergeometric2F1

  • To: mathgroup at smc.vnet.net
  • Subject: [mg93235] Re: [mg93156] Re: [mg93136] Hypergeometric2F1
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 1 Nov 2008 05:04:45 -0500 (EST)
  • References: <200810280954.EAA22098@smc.vnet.net> <200810291049.FAA09463@smc.vnet.net> <490ADB4D.6060901@csl.pl>

You seem to have missed some of you calculus classes, in particular,  
when the subject was Taylor's series (that is what + O[x]^5 in my code  
means).

(As form Fermat's Last Theorem; actually Mathematica knows it:

FullSimplify[x^n + y^n == z^n, Element[x | y | z | n, Integers] && n >  
2 && x y z != 0]
  False
)


Andrzej Kozlowski

On 31 Oct 2008, at 19:17, Artur wrote:

> 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
>>
>>
>>
>> __________ 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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