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I'd like to write the following equation:

Image of a mathematical equation.

I don't know which symbol is used for the P in the numerator. I have tried \mathcal{}, \mathfrak{}, and \mathsrc{}, but it wasn't any of these.

Could someone also recommend notation to describe the power density vector?

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It is the notation for ‘Weierstraß' elliptic function’, called ‘Weierstraß P’, and obtained with the command \wp. It is in particular used for the parameterisation of elliptic cubic curves.

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    On StackExchange, it's best to always create a new question, instead of adding questions in comments. You may, however, find that this post answers your question. – Coby Viner May 30 '19 at 18:02
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    You can increase it slighly with \mathlarger{\wp} (from the relsize package), or with something like, say, \text{\Large$\wp$}. – Bernard May 30 '19 at 18:02
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    @Bernard - Unless one is writing in german, it's perfectly ok to write "Weierstrass" rather than "Weierstaß". :-) – Mico May 30 '19 at 18:24
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    @Mico: Actually, I'd love to have the long s ligatures on my keyboard, but they seem to be unavailable… ;o) – Bernard May 30 '19 at 18:38
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    Yes, it should be used for the Weierstraß p function, but it's abused by several authors. – egreg May 30 '19 at 19:41
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As correctly indicated to you by the excellent users @barbara beeton both @Bernard the symbol to use is \wp. If I can help you, I have also inserted a code where I have used the clone of Times New Roman both in mathematical mode and in text mode.

enter image description here

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{newtxtext,newtxmath}
\begin{document}
\[D_H=\frac{\wp_{\max}}{P_{\text{rad}}/4\pi r^2}\]
\end{document}
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Additionally, the symbol ℘ for the Weierstrass elliptic function is in Unicode as U+2118. You can paste it directly into your source with unicode-math, of use \wp.

With legacy font packages, you can still define ℘ as \wp using newunicodechar (or inputenc).

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