Group Abstract Group Abstract

Message Boards Message Boards

0
|
4.6K Views
|
2 Replies
|
1 Total Like
View groups...
Share
Share this post:

Integral of Cauchy / Lorentzian distribution in Wolfram|Alpha

Posted 4 years ago
POSTED BY: Bastian Andersen
2 Replies

Thanks for the reply! I found similar last night, when setting y=1 and I=1 and taking the numerical integral, thus getting pi, and then doubling y / I.

Now I also realized my mistake... Missing a minus sign from the result from Wolfram|Alpha.

F(x) = Iyatan((x-x0)/y) + C In interval -inf...inf A = Iy(atan(inf)-atan(-inf)) A = Iypi

POSTED BY: Bastian Andersen
Posted 4 years ago

I'm going to assume that I is not the imaginary number but a positive real constant. Using Mathematica I get the following (after changing I to i which might be the issue with Wolfram|Alpha):

Integrate[i*y^2/((x - x0)^2 + y^2), {x, -\[Infinity], \[Infinity]}, Assumptions -> {x0 \[Element] Reals, y > 0, i > 0}]
(* i \[Pi] y *)
POSTED BY: Jim Baldwin
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard