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MathGroup Archive 1993

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Integral leading to Hypergeometric1F1

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Integral leading to Hypergeometric1F1
  • From: oliveria at engin.umich.edu
  • Date: Sun, 1 Aug 93 00:16:28 -0400

[this is a retransmission of a previous message with a
corrected From: line. -- smc]

I'm using MMA 2.2 on a decstation to solve the integral below.

<<Declare.m
Declare[n, Integer]
Declare[n, NonNegative]
Declare[V, Positive]
Declare[A, NonNegative]
Integrate[v^(2 n + 3) Exp[-v^2/V^2] / Sqrt[v^2 - A^2], {v,A,Infinity}]

                                                                 2
          3 + 2 n       3                        1    1         A
         V        Gamma[- + n] Hypergeometric1F1[-, -(-) - n, -(--)]
                        2                        2    2          2
                                                                V
Out[15]= ----------------------------------------------------------- + 
                                      2
 
                                                                          2
      3 + 2 n                  3                                5        A
     A        Sqrt[Pi] Gamma[-(-) - n] Hypergeometric1F1[2 + n, - + n, -(--)]
                               2                                2         2
                                                                         V
>    ------------------------------------------------------------------------
                                 2 Gamma[-1 - n]


Given the fact that n=0,1,2,.., and that A >= 0 and that V > 0 
(both A and V are finite real constants), can't I assume that
the second term in the answer above is always zero (since the
denominator goes to infinity) ? The use of some typical values
indicate that the second term indeed vanishes. Thus, is there a
way I can convince MMA to drop the second term (assuming it indeed
vanishes) ?

Recall that Hypergeometric1F1[2 + n, 5/2 + n, x] is entire function of x.

I also tried the integral above with Maple V.2 but it couldn't solve the
integral at all (or any of its variations). I did use the assume
facility do declare the types of n, A and V. Perhaps I need to load
some obscure macro library (which I'm not aware of).

Thanks.

  Roque
  oliveria at engin.umich.edu





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