Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 6th 2017
    • (edited Sep 6th 2017)

    I have added to step function statement and proof of its representation as

    Θ(x) =12πi e iωxωi0 + limε0 +12πi e iωxωiεdω, \begin{aligned} \Theta(x) & = \frac{1}{2\pi i} \int_{-\infty}^\infty \frac{e^{i \omega x}}{\omega - i 0^+} \\ & \coloneqq \underset{ \epsilon \to 0^+}{\lim} \frac{1}{2 \pi i} \int_{-\infty}^\infty \frac{e^{i \omega x}}{\omega - i \epsilon} d\omega \,, \end{aligned}

    (here).

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 6th 2017

    While I was it, I also added statement and proof that Θ=δ\partial \Theta = \delta (copied that also over to the Properties-section of delta distribution and to the Examples-section at derivative of distributions).

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 6th 2017

    step function (typo in your link)

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeSep 6th 2017

    Thanks, fixed now.