ZETA(3pm)

💖 ZETA 💖

okay bestie, so this is PDL::GSLSF::ZETA — it lives in section 3pm of the Perl manual (user contributed docs, we love a community moment 🫶). Pull up a chair, we're doing special functions.

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✨ NAME ✨

PDL::GSLSF::ZETA — it's the PDL interface to GSL Special Functions. that's it, that's the name. short, sweet, iconic. 👑

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🌸 DESCRIPTION 🌸

okay so basically? this is an interface to the Special Function package that lives inside the GNU Scientific Library. GSL said "here's the math" and PDL said "say less, I'll wrap it." and now you get to play with it. 💅

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🧚 FUNCTIONS 🧚

⭐ gsl_sf_zeta

here's the signature, no cap:

Signature: (double x(); double [o]y(); double [o]e())

this one's the Riemann Zeta Function:

zeta(x) = Sum[ k^(-s), {k,1,Infinity} ], s != 1.0

heads up bestie — see that s != 1.0? that's not a suggestion, that's the vibe check. s = 1.0 is not it. 🙈

and now the bad-value tea ☕: gsl_sf_zeta does not process bad values. what it will do is set the bad-value flag on all of your output ndarrays if that flag is set on any of the input ndarrays. so if one input is giving bad-value energy, the whole output group chat gets the flag. periodt. 🚩

🌈 gsl_sf_hzeta

signature time:

Signature: (double s(); double [o]y(); double [o]e(); double q)

this is the Hurwicz Zeta Function (yes, Hurwicz, not Riemann, they're different queens, know the difference):

zeta(s,q) = Sum[ (k+q)^(-s), {k,0,Infinity} ]

same energy as before, so let me repeat myself because it's important: gsl_sf_hzeta does not process bad values. and yeah — it sets the bad-value flag on all the output ndarrays whenever the flag is set for any of the input ndarrays. all of them. every single one. 🫶

🦋 gsl_sf_eta

signature, bestie:

Signature: (double x(); double [o]y(); double [o]e())

the Eta Function, and the formula is genuinely so cute, look at this:

eta(s) = (1-2^(1-s)) zeta(s)

it's literally just the zeta function wearing a little hat. obsessed. 🎀

aaaand you already know what I'm about to say: gsl_sf_eta does not process bad values, and it'll set the bad-value flag on all output ndarrays if the flag is set on any input ndarray. same rule, every time, no exceptions, iykyk. 💀

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👑 AUTHOR 👑

this file is copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> — All rights reserved. there is no warranty (sorry babes, that's the deal).

you are allowed to redistribute this software / documentation under certain conditions. for the details, go look at the file COPYING in the PDL distribution. 📄 and if this file ever gets separated from the PDL distribution, the copyright notice should be included in the file. don't leave it orphaned, it deserves better. 🥺

also: the GSL SF modules were written by G. Jungman. legend behavior, honestly. ⭐

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and that's the whole page bestie!! go compute some zetas, you're gonna slay 💖✨

this has been perl v5.38.2, dated 2024-04-10 — mwah, catch you on the next manpage 💅🎀