DILOG(3pm)

💖 DILOG 💖

okay bestie, so this is DILOG from the 3pm section — that's the User Contributed Perl Documentation shelf, iykyk — and it's living in PDL::GSLSF::DILOG. come sit with me, we're doing special functions today and honestly? it's giving math girlie. 🧚✨

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✨ NAME ✨

PDL::GSLSF::DILOG — the PDL interface to GSL Special Functions 🎀

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🌸 DESCRIPTION 🌸

so basically this is an interface to the Special Function package that lives inside the GNU Scientific Library. that's it, that's the vibe. it's a whole bridge between PDL and GSL's fancy math goodies. 💅

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👑 FUNCTIONS 👑

⭐ gsl_sf_dilog

Signature:

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

the Real part of DiLogarithm(x), for a real argument — no cap. in Lewin's notation this one is Li_2(x). and the way it's defined:

Li_2(x) = - Re[ Integrate[ Log[1-s] / s, {s, 0, x}] ]

🫶 heads up bestie: gsl_sf_dilog does not process bad values. it will set the bad-value flag of all output ndarrays if that flag is set for any of the input ndarrays. so like, one bad apple, whole bunch flagged. 🍓

🌈 gsl_sf_complex_dilog

Signature:

(double r(); double t(); double [o]re(); double [o]im(); double [o]ere(); double [o]eim())

this one is DiLogarithm(z), for a complex argument z = r Exp[i theta]. yes queen, complex. 💜

😭 same deal as before: gsl_sf_complex_dilog does not process bad values either. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

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💀 AUTHOR 💀

this file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it>. all rights reserved. there is no warranty — fr fr, none, zero, nada. 🙈

you're allowed to redistribute this software / documentation under certain conditions. for the deets, 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 be shady about it. 🎀

also, the GSL SF modules were written by G. Jungman. iconic of him. 👑

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alright that's the whole page, mwah 💋 — this was perl v5.38.2, dated 2024-04-10, filed under DILOG(3pm), and no you cannot borrow my notes without crediting me. slay, go compute something. ✨🦋