The letter ℘: name and origin? (2017)

    >>> import unicodedata
    >>> unicodedata.name('℘')
    'SCRIPT CAPITAL P'
    >>> ord('℘')
    8472

https://en.wikipedia.org/wiki/Letterlike_Symbols

Good enough for me.

Notably, this is distinct from ("MATHEMATICAL SCRIPT CAPITAL P").

> Books were printed in Fraktur, where the p looks quite normal, i.e., quite different from a handwritten Sütterlin p which could explain, why it hasn't been replaced in the publication of Amandus Schwarz.

Indeed. ("MATHEMATICAL FRAKTUR CAPITAL P") is also separate (but also, Unicode considers these mathematical symbols to exist separately from "text written in Fraktur script". So you get separate characters allocated for these symbols, but they're not intended to be suitable for printing in Fraktur - which is supposedly a presentation (i.e. typeface selection) issue.

Personally I'm not convinced that mathematical symbols derived from Latin or Greek (or other) scripts really have any claim to being separate "characters". Surely that's what variation selectors are for?

I think the answer by teika kazura on the linked page explains pretty thoroughly why this is not “good enough”. Most importantly:

> In Unicode the letter ℘ is given the codepoint U+2118 in the block "letterlike symbols", named "script capital p". But in fact it's lowercase.

Unicode technical note https://www.unicode.org/notes/tn27/ clarifies:

> Should have been called calligraphic small p or Weierstrass elliptic function symbol, which is what it is used for. It is not a capital "P" at all. A formal name alias correcting this to WEIERSTRASS ELLIPTIC FUNCTION has been defined.