[Date Index]
[Thread Index]
[Author Index]
Numerical evaluation of HypergeometricPFQ[{a,b,c},{d,e},1]
*To*: mathgroup at christensen.cybernetics.net
*Subject*: [mg497] Numerical evaluation of HypergeometricPFQ[{a,b,c},{d,e},1]
*From*: "NELSON M. BLACHMAN" <blachman at gtewd.mtv.gtegsc.com>
*Date*: Wed, 01 Mar 1995 22:28:48 PST
This is a postscript to my 26 February message (reproduced below)
complaining about Mma's not giving a numerical value for
HypergeometricPFQ[{1/2,1,1},{1.45,1.55},1].
I've since found that Mma does evaluate things like
HypergeometricPFQ[{1/2,1,1},{1.4,1.6},0.99999], but it takes
something like an hour on my 486DX33 PC--and it takes longer
and longer as the last argument gets closer and closer to 1.
So it's good that Mma quickly announces its inability to
compute HypergeometricPFQ[{1/2,1,1},{1.4,1.6},1].
A different method is evidently needed when the last argument is
1--provided that the sum of the components of the middle argument
exceeds the sum of the components of the first argument. (If not,
the hypergeometric function seems likely to be infinite.) So I
continue to hope for a formula for 3F2[{a,b,c},{d,e},1] as a
ratio of products of gamma functions of (e, f, and e + f minus
0, a, b, c, a + b, etc.), though I've so far been unable to
devise a satisfactory conjecture of this sort.
Nelson M. Blachman
>From: GTEWD::BLACHMAN "NELSON M. BLACHMAN" 26-FEB-1995 23:54:14.57
>To: MX%"mathgroup at christensen.cybernetics.net"
>CC: BLACHMAN
>Subj: Numerical Evaluation of HypergeometricPFQ
I was pleased to see just now that Mma's able to evaluate
Integrate[Sin[t u]/Sin[t],{t,0,Pi/2}] in terms of HypergeomtricPFQ.
When I asked it to plot the result, however, I found it apparently
unable to determine numerical values for HypergeomtricPFQ.
Maple can sometimes compute numerical values for HypergeomtricPFQ,
but for the particular denominator indices here it complains of
iteration limits' being exceeded. Does anyone know of a way to
get Mma 2.2 to evaluate HypergeomtricPFQ numerically?
I suspect there's a simple expression for HypergeomtricPFQ[{ },{ },1]
in terms of gamma functions when P = Q + 1; there is, anyhow, if
P = 2 and Q = 1. Does anyone know if that's true and, if so, what
it is?
Nelson M. Blachman
GTE Government Systems Corp.
Mountain View, California
Mathematica 2.2 for DOS 387
Copyright 1988-93 Wolfram Research, Inc.
In[1]:= Integrate[Sin[t u]/Sin[t],{t,0,Pi/2}]
3 u Pi u 1 3 - u 3 + u
(- + -) u Cos[----] HypergeometricPFQ[{-, 1, 1}, {-----, -----}, 1]
2 2 2 2 2 2
Out[1]= -------------------------------------------------------------------
3 u 1 u 1 u
4 (-(-) - -) (-(-) - -) (- - -)
2 2 2 2 2 2
In[2]:= f[t_]:= %1 /. u -> t Simplify ELIMINATES THE FIRST FACTOR IN
THE NUMERATOR AND IN THE DENOMINATOR.
In[3]:= f[.1] // N
Out[3]= 0.0997665 HypergeometricPFQ[{0.5, 1., 1.}, {1.45, 1.55}, 1.]
Next by Date:
**Numerical Evaluation of HypergeometricPFQ**
Next by thread:
**Re: Numerical evaluation of HypergeometricPFQ[{a,b,c},{d,e},1]**
| |