AIRY(3pm)

💫 AIRY — like, the PDL::GSLSF::AIRY page, bestie 💫

okay so this is AIRY(3pm) from the User Contributed Perl Documentation section of the manual, and it's literally all about the Airy functions. yes. those ones. sit down, we're doing math 🎀

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✨ NAME ✨

PDL::GSLSF::AIRY — 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 whole vibe. it's giving "glue code, but make it couture" 💅

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🦋 FUNCTIONS 🦋

ngl each one of these has the exact same signature, so once you clock it you're set for life. also every single one has the same bad-value behaviour, and I'm gonna tell you about it every time because the original does and I am nothing if not thorough 💖

⭐ gsl_sf_airy_Ai

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

Airy Function Ai(x). iconic. legendary. the moment 👑

gsl_sf_airy_Ai 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, it doesn't handle them, it just flags them. noted 📝

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🌈 gsl_sf_airy_Bi

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

Airy Function Bi(x). yes there are two of them. they're a duo. main character energy, both of them 💜

gsl_sf_airy_Bi 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_airy_Ai_scaled

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

Scaled Airy Function Ai(x). okay so the scaling is: Ai(x) for x < 0 and exp(+2/3 x^{3/2}) Ai(x) for x > 0. that exponential is doing SO much heavy lifting fr fr 🔥

gsl_sf_airy_Ai_scaled 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_airy_Bi_scaled

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

Scaled Airy Function Bi(x). same deal, but the B one: Bi(x) for x < 0 and exp(+2/3 x^{3/2}) Bi(x) for x > 0. 💖

gsl_sf_airy_Bi_scaled 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_airy_Ai_deriv

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

Derivative Airy Function Ai`(x). yep, that's a backtick, that's the prime, that's just how it's written, don't come for me 🙈

gsl_sf_airy_Ai_deriv 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_airy_Bi_deriv

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

Derivative Airy Function Bi`(x). the sequel. the derivative era. obsessed ✨

gsl_sf_airy_Bi_deriv 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_airy_Ai_deriv_scaled

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

Derivative Scaled Airy Function Ai(x). so: Ai`(x) for x < 0 and exp(+2/3 x^{3/2}) Ai(x)`` for x > 0. yes it's scaled and a derivative. she contains multitudes 💅

gsl_sf_airy_Ai_deriv_scaled 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_airy_Bi_deriv_scaled

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

Derivative Scaled Airy Function Bi(x). the final boss: Bi`(x) for x < 0 and exp(+2/3 x^{3/2}) Bi(x)`` for x > 0. 🎀

gsl_sf_airy_Bi_deriv_scaled 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 copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file.

The GSL SF modules were written by G. Jungman.

no warranty, bestie — say it with me — no warranty 😭

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and that's the whole page!! this one shipped as part of perl v5.38.2, dated 2024-04-10, so like, if you're citing it in your homework, that's the version and the date 💖 slay, go compute some Airy functions, you've got this 🦋