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Used in the proof of: | Used in the proof of: | ||
* The Cartesian product of two countable sets is countable | * The Cartesian product of two countable sets is countable | ||
Variations: | |||
* For spherical harmonics: | |||
{{ hidden | Spherical Harmonics | | |||
For spherical harmonics, we have <math>0 \leq |m| \leq l</math>. | |||
<math display="block"> | |||
\begin{equation} | |||
z = l(l+1) + m | |||
\end{equation} | |||
</math> | |||
<math display="block"> | |||
\begin{align} | |||
l &= \left\lfloor \sqrt{z} \right\rfloor\\ | |||
m &= z - x^2- x | |||
\end{align} | |||
</math> | |||
}} | |||