Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2006
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

Closed-form Integral Solution without Hypergeometric2F1Regularized ! ! !

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70219] Closed-form Integral Solution without Hypergeometric2F1Regularized ! ! !
  • From: "Jeffrey Tan" <M.L.Tan at open.ac.uk>
  • Date: Sat, 7 Oct 2006 07:09:06 -0400 (EDT)

Dear All,

I am trying to evaluate the definite integral of the following function, but
encountered the problem of Hypergeometric2F1Regularized.

Input       :   Integrate[x^n*Sqrt[(C + x)/(L - x)], {x, 0, L}, Assumptions ->
C &#8805; 0 && L &#8805; 0 && n &#8805; 0]

Output    :  \!\(If[C > 0 && L > 0, L\^n\ \@\(C\ L\)\ \@&#960;\  Gamma[1 + n]\
Hypergeometric2F1Regularized[\(-\(1\/2\)\), 
                  1 + n, 3\/2 + n, \(-\(L\/C\)\)], Integrate[x\^n\ \@\(\(C +
x\)\/\(L - \x\)\), {x, 0, L}, 
                 Assumptions -> C &#8804; 0 || L &#8804; 0]]\)

Here, for n = 0, 1, 2.... two conditions apply

1. L>= C >= 0, OR
2. C>= L >= 0 

However, suppose I put n = 0, 1, 2,...10 individually in the integration,  I'll
get a closed-form solution without the complexity of
Hypergeometric2F1Regularized.

Could anyone suggest any possibility of avoiding the presence of
"Hypergeometric2F1Regularized", in order to make the integral more
approachable in calculation? Many thanks in advance.

Cheers,

Jeffrey M.L.Tan


  • Prev by Date: Re: Bessel K expansion, large argument?
  • Next by Date: Re: Possible bug in Histogram
  • Previous by thread: Re: Troubles with Integrate
  • Next by thread: Re: Closed-form Integral Solution without Hypergeometric2F1Regularized ! ! !