FERMI_DIRAC(3pm)

💖 FERMI_DIRAC 💖

okay bestie, welcome to PDL::GSLSF::FERMI_DIRAC — that's the PDL interface to GSL Special Functions, she's a User Contributed Perl Documentation girlie and honestly? iconic. 🎀

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✨ NAME ✨

PDL::GSLSF::FERMI_DIRAC — the PDL interface to GSL Special Functions, no cap.

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🌸 DESCRIPTION 🌸

So this is literally an interface to the Special Function package that lives inside the GNU Scientific Library. And before you run off, please note that:

Complete Fermi-Dirac Integrals:

 F_j(x)   := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]

Incomplete Fermi-Dirac Integrals:

 F_j(x,b) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,b,Infinity}]

that's the whole vibe. math but make it quantum stats. ✨

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🔥 FUNCTIONS 🔥

gsl_sf_fermi_dirac_int

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

complete integral F_j(x) for integer j — she's giving full integral, full slay. 💅

gsl_sf_fermi_dirac_int does not process bad values. she will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. so like. handle your bad values yourself bestie. 💀

gsl_sf_fermi_dirac_mhalf

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

complete integral F_{-1/2}(x) — negative half, main character energy tbh. 🦋

gsl_sf_fermi_dirac_mhalf 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. 🫶

gsl_sf_fermi_dirac_half

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

complete integral F_{1/2}(x) — the half girlie, we love her. 🌸

gsl_sf_fermi_dirac_half 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. 💖

gsl_sf_fermi_dirac_3half

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

complete integral F_{3/2}(x) — three halves?? she ate that. 🔥

gsl_sf_fermi_dirac_3half 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. 🌈

gsl_sf_fermi_dirac_inc_0

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

incomplete integral F_0(x,b) = ln(1 + e^(b-x)) - (b-x) — incomplete but never incomplete in our hearts. 😭

gsl_sf_fermi_dirac_inc_0 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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👑 AUTHOR 👑

this file is copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> — all rights reserved, and ngl there is no warranty, fr fr. 🙈

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. keep the receipts, bestie. 🧚

the GSL SF modules were written by G. Jungman. king behavior honestly. 👑

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💜 and that's the whole page, periodt.

this page was brought to you by perl v5.38.2, dated 2024-04-10 — a little vintage moment, a lil throwback, and she still slays. bye bestie, go compute some integrals 🎀✨💅