integration of rational functions with parameter; simplification. Limit
- To: mathgroup at smc.vnet.net
- Subject: [mg41599] integration of rational functions with parameter; simplification. Limit
- From: Richard Fateman <fateman at cs.berkeley.edu>
- Date: Wed, 28 May 2003 04:57:30 -0400 (EDT)
- Organization: University of California, Berkeley
- Sender: owner-wri-mathgroup at wolfram.com
in Mathematica 4.1, I tried integrating (a*x+b)/(c*x^2+d*x+e)^n and got a rather large answer involving AppelF1 and Hypergeometric functions. Indeed, differentiating that answer and FullSimplifying gets back to the start. So it seems to be An integral. There are, of course many such indefinite integrals, differing by a constant. So it is not impossible, but yet quite inconvenient, for the large answer to be useless (e.g. unbounded) for any particular value of n. It might even be useless for all values of n. Like substituting n=1 gives an error (1/0 generated) and even taking limits as n->1 gives the peculiar result... (b*c*e*Infinity)/(Sqrt[Sign[d^2 - 4*c*e]]* Sign[-d + Sqrt[d^2 - 4*c*e]]* Sign[d + Sqrt[d^2 - 4*c*e]]) This seems to suggest that if none of b,c,e are zero, the answer is Infinity; if one of them is zero, the answer is zero. If one tries FullSimplify[answer], and THEN takes the derivative, the path back to the original integrand seems to be blocked. What to do? It may be that the answer is bogus, having a "constant" that is somehow a singular function of n, or the simplification functions are inadequate (actually, not much question of this). The result of Limit could be better.