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
>