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>*Reply-to*: grafix at csl.pl

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 > > > >