0
|
5382 Views
|
3 Replies
|
1 Total Likes
View groups...
Share
GROUPS:

# Another integration problem

Posted 10 years ago
 Hi,I wanted to integrate this:Integrate[Simplify[  Exp[-2*(m*c/hbar)*x*r] * (1 + 1/(2*x^2)) * (x^2 - 1)^(1/2) / x^2,  {x, r, m, c, hbar} > 0 && {x, r, m, c, hbar} \[Element] Reals], {x,   1, Infinity}]where m,c,hbar are constants defined like thism := 9.10938291*10^-28hbar := 1.054571726*10^-27c := 29979245800andris a parameter.I tried to put in some simplifying assumtion that all values are Real and Positive in order to help solve the integral.However the result of the integration is:ConditionalExpression[ 6.10161*10^10 r + 1.81857*10^31 r^3 +   2.4674 MeijerG[{{}, {1/2, 3/2}}, {{0, 0}, {1/2, 1/2}},     6.70605*10^20 r^2] +   1.2337 MeijerG[{{}, {1/2, 5/2}}, {{0, 1}, {1/2, 1/2}},     6.70605*10^20 r^2], Re[r] > 0]So I was wondering if I miss something which causes the integration to result in this complicated conditional expression (for which I have no idea what it means).In case some context might be of help: I'm trying to solve the integral part of Eq.1 of this paper: http://cds.cern.ch/record/966452/files/PhysRev.95.1048.pdfAny ideas anyone ?
3 Replies
Sort By:
Posted 10 years ago
 Correct syntax will help here.Integrate[ Exp[-2*(m*c/hbar)*x*r]*(1 + 1/(2*x^2))*(x^2 - 1)^(1/2)/x^2, {x, 1,  Infinity}, Assumptions -> Thread[{r, m, c, hbar} > 0]]Alternatively, give those constants the intended values. The integral will evaluate much faster.m = 9.10938291*10^-28;hbar = 1.054571726*10^-27;c = 29979245800;Integrate[ Exp[-2*(m*c/hbar)*x*r]*(1 + 1/(2*x^2))*(x^2 - 1)^(1/2)/x^2, {x, 1,  Infinity}, Assumptions -> r > 0]Better might be to remove the constants, since they only are used with r, and put them back later.Integrate[ Exp[-2*(m*c/hbar)*x*r]*(1 + 1/(2*x^2))*(x^2 - 1)^(1/2)/x^2, {x, 1,  Infinity}, Assumptions -> Thread[{r, m, c, hbar} > 0]] /. r->(m*c/hbar)*r
Posted 10 years ago
 ah thank you very much. yes, i'm still struggling a lot with the syntax :/
Posted 10 years ago
 Xort, the following form should workm := 9.10938291*10^-28hbar := 1.054571726*10^-27c := 29979245800function = Exp[(-2*(m*c/hbar)*x*r)]*(1 + 1/(2*x^2))*(x^2 - 1)^(1/2)/x^2Integrate[function, {x, 1, Infinity}]