Re: Solving double integral without Error function

*To*: mathgroup at smc.vnet.net*Subject*: [mg57724] Re: Solving double integral without Error function*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Mon, 6 Jun 2005 04:21:33 -0400 (EDT)*Organization*: The University of Western Australia*References*: <d7rk3i$bkt$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <d7rk3i$bkt$1 at smc.vnet.net>, "Xavier Brusset" <brusset at poms.ucl.ac.be> wrote: > I have to solve this double integral: > Phi[ q_ ]=Integrate[Integrate[y(x-q)f[x,y],{x,0,q}],{y,2,15}] > where > f[ x_ , y_ ]=1/(2 Pi Sqrt[27])Exp{-1/54 [4 x^2 - 6yx - 50x + 9y^2 -30 y + > 325]} There is a syntax error here in your definition of f. > Mathematica 5.1 on windows fumbles a lot and finally stops giving an answer > in q but using the Error function (I am using the Statistics Continuous > distributions module). That is irrelevant. Integrating exponentials of quadratic functions will lead to Erf. In general, there is no simple closed form for a second (indefinite) integral. > The problem with the Error function is that when I combine this function Phi > into another equation, I can't find a root in q. > Which function of Mathematica should I use which circumvents the Error > function in solving the double integral? > Or, alternately, which root finding function could I use to find even a > numeric instance of q? There is a simple alternative way of proceeding. It is straightforward to compute the first and second derivatives of Phi with respect to q. You can use this with NDSolve to compute Phi[q]. See http://physics.uwa.edu.au/pub/Mathematica/MathGroup/ErfIntegral.nb Cheers, Paul -- Paul Abbott Phone: +61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) AUSTRALIA http://physics.uwa.edu.au/~paul http://InternationalMathematicaSymposium.org/IMS2005/