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MathGroup Archive 1995

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Numerical Evaluation of HypergeometricPFQ

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg492] Numerical Evaluation of HypergeometricPFQ
  • From: "NELSON M. BLACHMAN" <blachman at gtewd.mtv.gtegsc.com>
  • Date: Sun, 26 Feb 1995 23:54:13 PST

  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 HypergeomPFQ.  
When I asked it to plot the result, however, I found it apparently 
unable to determine numerical values for HypergeomPFQ.  

  Maple can sometimes compute numerical values for HypergeomPFQ, 
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 HypergeomPFQ numerically?

  I suspect there's a simple expression for HypergeomPFQ[{ },{ },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.]



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