someone help me

Thread Starter

bluster

Joined Dec 14, 2006
2
Hi,
Please can someone help me with this problem:

Find the solution of the:

1) ∫ exp -X^2 erf(p_x) dx (0<x<p)

2) ∫ exp -pX^2 erf(ax) dx (0<x<infinity)

3) ∫ exp -pX^2 erf(ax) erf(bx) dx (0<x<infinity)
 

Dave

Joined Nov 17, 2003
6,970
Hi,
Please can someone help me with this problem:

Find the solution of the:

1) ∫ exp -X^2 erf(p_x) dx (0<x<p)

2) ∫ exp -pX^2 erf(ax) dx (0<x<infinity)

3) ∫ exp -pX^2 erf(ax) erf(bx) dx (0<x<infinity)
For 1): Use the identity View attachment 402 (ref. D'Orsonga 2005)

For 2) and 3); use the identity View attachment 403 (ref. Prudnikov 1990)

If you want a derivation from first principles then you will probably need to look at using the error function substitution and using brute force to get the answer.

View attachment 404

Gifs courtesy of mathworld.wolfram.com

Dave
 

Dave

Joined Nov 17, 2003
6,970
For 2) and 3); use the identity View attachment 403 (ref. Prudnikov 1990)
Apologies, for 2) and 3); use the identity View attachment 403 = View attachment 405(ref. Prudnikov 1990)

As for solving the equations, you are probably advised to look at the world of both D'Orsonga and Prudnikov (ref http://mathworld.wolfram.com/Erf.html for details of the paper titles).

My approach to this would be either to use the error function subsistion I gave in my previous post and perform a fully integral on e^-(t^2) before performing the integral of the solution using parts. The other appraoch is to use the Maclaurin Series of the error function: View attachment 406

And multiply out the integral and perform a series of smaller and simpler integrals.

Dave
 
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