𝓙. 𝓜. on Nostr: as someone who works with "special functions": I have a feeling someone (or multiple ...

as someone who works with "special functions": I have a feeling someone (or multiple someones) is conflating "algebraic" with "elementary". Let me explain, starting with an analogy: in the so-called "casus irreducibilis" of cubic equations, we readily accept the use of trigonometric or hyperbolic functions (certainly elementary!) to represent the roots of a cubic polynomial. For quintics, we need theta functions or hypergeometric functions, which are most assuredly not elementary, but evaluate to algebraic numbers. (Then we need Riemann theta for roots of polynomials of even higher order!)