/sci/ - Science & Math

[Anonymous No.8764151]

please show me a function that is not absolutely integrable but is square integrable

[Anonymous No.8764175]

>>8764151
[math]|x|^{-1/2} / (1+x^2)[/math]

[Anonymous No.8764181]

>>8764175
oops that's the opposite

[Anonymous No.8764230]

>>8764151

[math]f : x \mapsto
\begin{cases}
1 \ \mathrm{if} \ x \in [-1,1] \\
\frac{1}{|x|} \ \mathrm{if} \ |x|>1
\end{cases}[/math]

[Anonymous No.8764767]

>>8764230

unconditional functions only.

[Anonymous No.8764776]

>>8764767
>unconditional functions only.

[Anonymous No.8764782]

>>8764767
unconditinally funny

[Anonymous No.8764802]

>>8764767
[eqn] f(x) = \frac{1}{2} \left( \frac{1}{|x|} + 1 - \left| 1 - \frac{1}{|x|} \right| \right) [/eqn]

Which is exactly the same function as >>8764230

[Anonymous No.8764864]

>>8764802
Cool, I was thinking on how to rewrite it using the absolute value.

[Anonymous No.8765502]

>>8764802
this still is a conditional function
|x| = x if x > 0 else -x

[Anonymous No.8765517]

>>8765502
tough fucking luck

[Anonymous No.8765524]

>>8764767
>unconditional functions only
[math]f(x)=\frac{e^{-\frac{1}{x^2}}}{x}[/math]

[Anonymous No.8765702]

[eqn] \frac{x}{1 + x^2} [/eqn]

[Anonymous No.8765752]

>>8764151
1/n with the counting measure.

[Anonymous No.8765950]

>>8764767

Unconditionnal kek

[Anonymous No.8766438]

[math]f(x) = \frac12 \left( \frac{1}{ \sqrt{x^2}}+1-\sqrt{ \left( 1-\frac{1}{\sqrt{x^2}} \right)^2} \right)[/math]

which is exactlye the same function as
>>8764802