Re: limit
- To: mathgroup at smc.vnet.net
- Subject: [mg78650] Re: limit
- From: chuck009 <dmilioto at comcast.com>
- Date: Fri, 6 Jul 2007 03:22:14 -0400 (EDT)
Hey Daniel. I felt we couldn't use L'Hopital's rule since f2 was not differentiable over an open interval containing the point s=1. This I concluded by plotting: f2 = 1/HypergeometricPFQ[{1/4 + s/4, 1/4 + s/4, 1/ 4 + s/4, 3/4 + s/4}, {1/2, 1, 1}, 1] Plot[f2, {s, 0.9, 1.1}, Axes -> None] Note the kink in the plot at s=1. Perhaps you could clarify this for me please. Thanks! > I think the limit is -Infinity. > > consider the following trick : > > f1=2^(-2+s)*Cos[(1/4)*Pi*(1+s)]*Gamma[(1+s)/4]^2*Gamma > [(1+s)/2] > > f2= 1/HypergeometricPFQ[{1/4 + s/4, 1/4 + s/4, 1/4 + > s/4, 3/4 + s/4}, > > {1/2, 1, 1}, 1] > > then we are interessted in the limit of f1/f2. As > both these expressions > > are 0 for s=1, we can take the quotient of the > drivatives: > > D[f1,s]=-\[Pi]^2/8 > > D[f2,s]= 0 > > therefore we get -Infinity > > hope this helps, Daniel >