limit
- To: mathgroup at smc.vnet.net
- Subject: [mg78538] limit
- From: dimitris <dimmechan at yahoo.com>
- Date: Tue, 3 Jul 2007 06:52:30 -0400 (EDT)
Hello.
Say
In[88]:=
o = -((2^(-2 + s)*Cos[(1/4)*Pi*(1 + s)]*Gamma[(1 + s)/4]^2*Gamma[(1 +
s)/2]*
HypergeometricPFQ[{1/4 + s/4, 1/4 + s/4, 1/4 + s/4, 3/4 + s/4},
{1/2, 1, 1}, 1])/Pi);
I am interested in the value at (or as s->) 1.
I think there must exist this value (or limit) at s=1.
In[89]:=
(N[#1, 20] & )[(o /. s -> 1 - #1 & ) /@ Table[10^(-n), {n, 3, 10}]]
Out[89]=
{-0.12528902994360074335,-0.12502887873817160412,-0.12500288763144810876,-0.\
12500028876072131305,-0.12500002887604789652,-0.12500000288760454730,-0.\
12500000028876045231,-0.12500000002887604521}
However both
o/.s->1
and
Limit[o,s->1,Direction->1 (*or -1*)]
does not produce anything.
Note also that
In[93]:=
2^(-2 + s)*Cos[(1/4)*Pi*(1 + s)]*Gamma[(1 + s)/4]^2*Gamma[(1 + s)/
2] /. s -> 1
HypergeometricPFQ[{1/4 + s/4, 1/4 + s/4, 1/4 + s/4, 3/4 + s/4}, {1/2,
1, 1}, 1] /. s -> 1
Out[93]=
0
Out[94]=
Infinity
So am I right and the limit exist (if yes please show me a way to
evaluate it) or not
(in this case explain me why; in either case be kind if I miss
something fundamental!)
Thanks
Dimitris