# Question:How to perform numerical intergration with a gamma function

## Question:How to perform numerical intergration with a gamma function

Maple

Hello all,

I need to perform this numerical integration through maple. Having been a complete beginner I just wanted to ask if at all this is feasible using maple? I have done similar stuff using mathematica, but would like to try and calculate the same using maple, especially with the gamma function in the above equation.

W_{-} := M*sqrt(Pi)/(2*A*a)*(x*erf(a*x) + (1/(a*sqrt(Pi)))*exp(-a^2*x^2)) + (M/(A*a*sqrt(Pi)))*evalf(Int(exp(-epsilon^2/(4*a^2) - tau*epsilon^3)*(cos(epsilon*x) - 1)/epsilon^2, epsilon = 0..infinity)) + (2*m/Pi)*evalf(Int(exp(-tau*epsilon^3)*(cos(epsilon*x) - 1)/epsilon^2, epsilon = 0..infinity)) + (M/(A*a*sqrt(Pi)))*evalf(Int((1/(2*a^2) + 3*tau*epsilon)*exp(-epsilon^2/(4*a^2) - tau*epsilon^3), epsilon = 0..infinity)) - (2*m/Pi)*tau^(1/3)*GAMMA(2/3) -m*x;

W_{+} := M*sqrt(Pi)/(2*A*a)*(x*erf(a*x) + (1/(a*sqrt(Pi)))*exp(-a^2*x^2)) + (M/(A*a*sqrt(Pi)))*evalf(Int(exp(-epsilon^2/(4*a^2) - tau*epsilon^3)*(cos(epsilon*x) - 1)/epsilon^2, epsilon = 0..infinity)) + (2*m/Pi)*evalf(Int(exp(-tau*epsilon^3)*(cos(epsilon*x) - 1)/epsilon^2, epsilon = 0..infinity)) + (M/(A*a*sqrt(Pi)))*evalf(Int((1/(2*a^2) + 3*tau*epsilon)*exp(-epsilon^2/(4*a^2) - tau*epsilon^3), epsilon = 0..infinity)) - (2*m/Pi)*tau^(1/3)*GAMMA(2/3) + m*x;

M := 6.3*10^{17};

t := 7200;

a := 10^3 ;

m := 1;

D := 10^{-5};

Omega := 1.7*10^{23}

tau := 10^{-14}

A := tau/(D*Omega*t);

Any suggestions as how to proceed would be very helpful. Thanks.

EDIT: I would like plot the functions W_{+} and W_{-} as a function of x-axis, with both representing either side of x=0.

EDIT: for some reason I cannot reply to the comments but I have modified the question based on the comments below.

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