PSI(3pm)

💖 PSI(3pm) 💖

okay bestie, gather round, because this one is called PDL::GSLSF::PSI and it's a Perl module — specifically the PDL interface to GSL Special Functions. yes. the math kind. stay with me, it's actually gorgeous. 🎀

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✨ NAME ✨

PDL::GSLSF::PSI — your girl is the PDL interface to GSL Special Functions. that's the whole name, that's the whole vibe. 🦋

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🌸 DESCRIPTION 🌸

so this is an interface to the Special Function package that lives inside the GNU Scientific Library. iconic library, no notes. 💅

now, the Poly-Gamma Functions part, which is where it gets spicy:

psi(m,x) := (d/dx)^m psi(0,x) = (d/dx)^{m+1} log(gamma(x))

like, look at her. the m-th derivative of psi of zero, x, equals the (m+1)-th derivative of log of gamma of x. periodt. ✨

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🧚 FUNCTIONS 🧚

💜 gsl_sf_psi

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

this one is the Di-Gamma Function psi(x). that's it, that's the function, she's just psi of x. 🫶

⚠️ real talk though: gsl_sf_psi does not process bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. so like, one bad input and the whole friend group gets flagged. 😭

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🌈 gsl_sf_psi_1piy

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

this cutie gives you the Di-Gamma Function Re[psi(1 + I y)] — that's the real part of psi of one plus i times y, in case the imaginary part was trying to be the main character. 💅

⚠️ same energy as above, bestie: gsl_sf_psi_1piy does not process bad values. 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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⭐ gsl_sf_psi_n

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

and THIS one, the moment you've been waiting for, is the Poly-Gamma Function psi^(n)(x). yes it takes an extra int n, because she's fancy. 👑

⚠️ and yes, same rule, we keep it consistent: gsl_sf_psi_n does not process bad values. it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. the way that bad-value flag just ✨propagates✨. 💀

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👑 AUTHOR 👑

this file is copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it>. all rights reserved, bestie. 🎀

🚨 there is no warranty. like, none. zero. the math might be perfect but the warranty is not included. 😭

you are 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 leave her orphaned, she's sensitive. 🥺

also, the GSL SF modules were written by G. Jungman. credit where credit is due, we love a collaborator. 🫶

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🌸 cute lil sign-off 🌸

this page came from perl v5.38.2, dated 2024-04-10, and it's the PSI(3pm) manual page — third section, Perl module, and it ate. mwah. 💖✨🎀🦋💅