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Question: Obtaining an analytical solution for a specific integral

Question:Obtaining an analytical solution for a specific integral

ntnu 0 Maple
integral int
February 08 2012
0

We are trying to obtain an analytical solution of an integral in Maple. When solved numerically the integral converges, but we are not able to get an analytical solution. Any ideas?

The constants in the integral is computed independently, not sure if knowing them can help. The values are r=0.06, kappa=2.6, myksi=2.18, rho=-0.21, stdk=382.2, stds=47.8, kji=52.9 and ksi=62.3. We kind of need the analytical solution to handle the expression in further calculations, and therefore would like to keep the variable names in the solution.

One idea could be that e^-r(x-t) is the reason why the integral converges numerically, but assuming that 0<r<1 did not improve anything.

Any help would be appreciated!

 

int(exp(-r*(x-t))*(sqrt(stdk^2*(1-exp(-2*kappa*(x-t)))/(2*kappa)+stdk^2*(x-t)+(2*(1-exp(-kappa*(x-t))))*rho*stdk*stds/kappa)*exp(-(E-exp(-kappa*(x-t))*kji-ksi-myksi*(x-t))^2/(2*(stdk^2*(1-exp(-2*kappa*(x-t)))/(2*kappa)+stdk^2*(x-t)+(2*(1-exp(-kappa*(x-t))))*rho*stdk*stds/kappa)))/sqrt(2*Pi)+(exp(-kappa*(x-t))*kji+ksi+myksi*(x-t)-E)*(1/2-(1/2)*erf((E-exp(-kappa*(x-t))*kji-ksi-myksi*(x-t))/sqrt(2*stdk^2*(1-exp(-2*kappa*(x-t)))/(2*kappa)+stdk^2*(x-t)+(2*(1-exp(-kappa*(x-t))))*rho*stdk*stds/kappa)))), x = t .. infinity)

int(exp(-r*(x-t))*((1/4)*(2*stdk^2*(1-exp(-2*kappa*(x-t)))/kappa+4*stdk^2*(x-t)+8*(1-exp(-kappa*(x-t)))*rho*stdk*stds/kappa)^(1/2)*exp(-(E-exp(-kappa*(x-t))*kji-ksi-myksi*(x-t))^2/(stdk^2*(1-exp(-2*kappa*(x-t)))/kappa+2*stdk^2*(x-t)+4*(1-exp(-kappa*(x-t)))*rho*stdk*stds/kappa))*2^(1/2)/Pi^(1/2)+(exp(-kappa*(x-t))*kji+ksi+myksi*(x-t)-E)*(1/2-(1/2)*erf((E-exp(-kappa*(x-t))*kji-ksi-myksi*(x-t))/(stdk^2*(1-exp(-2*kappa*(x-t)))/kappa+stdk^2*(x-t)+2*(1-exp(-kappa*(x-t)))*rho*stdk*stds/kappa)^(1/2)))), x = t .. infinity)

 (1)

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