Understanding the Role of Error Functions in Integrals

[maverick_76]

Okay so I was integrating an expression and ended up getting an imaginary error function in the answer. I'm not sure where to go from there, I plugged it into wolfram and the root it gave me looks nice but is that worth anything to me?

The integral was being evaluated from -∞ to ∞, would I need to evaluate the error function from these limits or is the root what I'm looking for?

 

[maverick_76]

Here is the original integral and resulting error function

 

[mathman]

If you want the infinite integral a better approach is to complete the square (in k) of the exponent. net result is I = e^{\frac{-x^2}{4b}}\sqrt{\frac{\pi}{b}}.

Comment: All you are doing is taking the Fourier transform of a normal curve.

 

[maverick_76]

Okay that makes sense. Thanks!