MathGroup Archive 2007

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: limit

  • To: mathgroup at smc.vnet.net
  • Subject: [mg78545] Re: limit
  • From: dh <dh at metrohm.ch>
  • Date: Wed, 4 Jul 2007 05:28:36 -0400 (EDT)
  • References: <f6d9si$2l5$1@smc.vnet.net>


Hi Dimitris,

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





dimitris wrote:

> 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

> 

> 




  • Prev by Date: Re: Logics and probability
  • Next by Date: Re: Re: Rotable Graphics and ViewPoint
  • Previous by thread: limit
  • Next by thread: Re: Re: limit