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