Re: Re: Hypergeometric2F1

*To*: mathgroup at smc.vnet.net*Subject*: [mg93195] Re: [mg93156] Re: [mg93136] Hypergeometric2F1*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Thu, 30 Oct 2008 02:04:43 -0500 (EST)*References*: <200810280954.EAA22098@smc.vnet.net> <200810291049.FAA09463@smc.vnet.net> <49086272.5090408@csl.pl>

I am amazed that someone would actually write this sort of thing without bothering to execute the code that was actually posted. LogicalExpand[ArcCosh[2]/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[3]*ArcCosh[2]) + 4/(27*ArcCosh[2]^2) + 1/(3*Sqrt[3]*ArcCosh[2]^3) + 1/(9*ArcCosh[2]^4) == 0 && -((a*(a + 1)*(a + 2)*b*(b + 1)*(b + 2))/ (6*c*(c + 1)*(c + 2))) + 1/(6*Sqrt[3]*ArcCosh[2]) + 2/(9*ArcCosh[2]^2) + 1/(3*Sqrt[3]*ArcCosh[2]^3) == 0 && -((a*(a + 1)*b*(b + 1))/(2*c*(c + 1))) + 1/(3*Sqrt[3]*ArcCosh[2]) + 1/(3*ArcCosh[2]^2) == 0 && 1/(Sqrt[3]*ArcCosh[2]) - (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[1]: 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[1]:{0.297, FindInstance[9/5 - Hypergeometric2F1[1/4, 1/2, c, > 80/81] == 0, > c]} > > good answer is c=3/4 > > Because FindInstance crash on one parameter equation from these > reason we can be 100% sure that also crash on 3 parameters equation. > > From these reason I was ask about interpolating function/propcedure > 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[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 >> >> >> >>

**References**:**Hypergeometric2F1***From:*Artur <grafix@csl.pl>

**Re: Hypergeometric2F1***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>