{\displaystyle f(x)={\frac {1}{x}}\sin \left({\frac {1}{x^{3}}}\right).}f(x)={\frac {1}{x}}\sin \left({\frac {1}{x^{3}}}\right).
This function has a singularity at 0, and is not Lebesgue integrable. However, it seems natural to calculate its integral except over the interval [−ε, δ] and then let ε, δ → 0.
Still not working 100% for me.
When I copy from “This integral” to “…δ → 0” it doesn’t display the $$\frac{1}{x} sin(\frac{1}{x^3})$$ equation properly:
This integral was first defined by Arnaud Denjoy (1912). Denjoy was interested in a definition that would allow one to integrate functions like
This function has a singularity at 0, and is not Lebesgue integrable. However, it seems natural to calculate its integral except over the interval [−ε, δ] and then let ε, δ → 0.
When I start copying with the equation, the equation displays properly, but it is an image link, not Markdown:
This function has a singularity at 0, and is not Lebesgue integrable. However, it seems natural to calculate its integral except over the interval [−ε, δ] and then let ε, δ → 0.
and when I copy just the equation, I get an image, as expected.
The inline equations also don’t work for me:
we define the Riemann sum for a function {\displaystyle f\colon [a,b]\to \mathbb {R} } to be
I just put the latex in $$$$, and the text below in one block.
this is the block:
$${\displaystyle f(x)={\frac {1}{x}}\sin \left({\frac {1}{x^{3}}}\right)}$$
This function has a singularity at 0, **and** **is** **not** Lebesgue integrable. However, it seems natural to calculate its integral except over the interval [−ε, δ] **and** then **let** ε, δ → 0.
ok, I see. So one still has to edit every formula by hand. I was hoping to find something automatic, especially for text with lots of in-line formulas.
I just wrote a feature request for smart pasting to allow user-defined regexps and callbacks to be run during paste for capturing google maps links, but now I realize that this would also make it easy to recognize Wikipedia math and turn it into proper Markdown.