BESSEL(3pm)

💖 BESSEL(3pm) — PDL::GSLSF::BESSEL 💖

okay so this is the BESSEL(3pm) page from the User Contributed Perl Documentation collection, and bestie, it's literally a whole bouquet of Bessel functions. 🌸

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🎀 NAME 🎀

PDL::GSLSF::BESSEL — 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 the whole vibe. 💅

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🧚 FUNCTIONS 🧚

Every single one of these is a Bessel-adjacent legend, and every single one has the same little quirk about bad values (more on that in a sec). Let's go, one by one. 🫶

gsl_sf_bessel_Jn

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

Regular Bessel Function J_n(x). The classic. The blueprint. 👑

🚩 gsl_sf_bessel_Jn does not process bad values. If the bad-value flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays. that's just how it is, no cap.

gsl_sf_bessel_Jn_array

Signature: (double x(); double [o]y(num); int s; int n=>num)

An array of Regular Bessel Functions, from J_{s}(x) all the way to J_{s+n-1}(x). it's giving buy one get a whole row. 🌈

🚩 gsl_sf_bessel_Jn_array does not process bad values, and if the bad-value flag is set for any of the input ndarrays it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_Yn

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

IrRegular Bessel Function Y_n(x). the chaotic sibling, we love them. 💜

🚩 gsl_sf_bessel_Yn does not process bad values — if the flag is set for any input ndarray, the bad-value flag gets set on all the output ndarrays.

gsl_sf_bessel_Yn_array

Signature: (double x(); double [o]y(num); int s; int n=>num)

An array of Regular Bessel Functions from Y_{s}(x) to Y_{s+n-1}(x). ✨

🚩 gsl_sf_bessel_Yn_array does not process bad values. Bad-value flag set on any input ndarray? Then it's set on all the output ndarrays. periodt.

gsl_sf_bessel_In

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

Regular Modified Bessel Function I_n(x). ✨

🚩 gsl_sf_bessel_In does not process bad values, and it will set the bad-value flag of all the output ndarrays if that flag is set for any of the input ndarrays.

gsl_sf_bessel_I_array

Signature: (double x(); double [o]y(num); int s; int n=>num)

An array of Regular Modified Bessel Functions, I_{s}(x) through I_{s+n-1}(x). 🦋

🚩 gsl_sf_bessel_I_array does not process bad values. If the bad-value flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_In_scaled

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

Scaled Regular Modified Bessel Function exp(-|x|) I_n(x). look at that scaling, she's thriving. 💅

🚩 gsl_sf_bessel_In_scaled does not process bad values — and yeah, if the bad-value flag is set for any input ndarray it will set that flag on all the output ndarrays.

gsl_sf_bessel_In_scaled_array

Signature: (double x(); double [o]y(num); int s; int n=>num)

An array of Scaled Regular Modified Bessel Functions, exp(-|x|) I_{s}(x) all the way up to exp(-|x|) I_{s+n-1}(x). 🌟

🚩 gsl_sf_bessel_In_scaled_array does not process bad values. Bad-value flag set on any of the input ndarrays → set on all the output ndarrays.

gsl_sf_bessel_Kn

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

IrRegular Modified Bessel Function K_n(x). the moody one, honestly iconic. 💜

🚩 gsl_sf_bessel_Kn does not process bad values. If the bad-value flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_K_array

Signature: (double x(); double [o]y(num); int s; int n=>num)

An array of IrRegular Modified Bessel Functions, K_{s}(x) to K_{s+n-1}(x). 🔥

🚩 gsl_sf_bessel_K_array does not process bad values — bad-value flag on any input ndarray means bad-value flag on all the output ndarrays.

gsl_sf_bessel_Kn_scaled

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

Scaled IrRegular Modified Bessel Function exp(-|x|) K_n(x). 💫

🚩 gsl_sf_bessel_Kn_scaled does not process bad values. If the bad-value flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_Kn_scaled_array

Signature: (double x(); double [o]y(num); int s; int n=>num)

An array of Scaled IrRegular Modified Bessel Functions, exp(-|x|) K_{s}(x) through exp(-|x|) K_{s+n-1}(x). 🎀

🚩 gsl_sf_bessel_Kn_scaled_array does not process bad values — if the flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_jl

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

Regular Sphericl Bessel Function J_n(x). (lowercase jl, note the lowercase, bestie — she's the spherical one 🌐)

🚩 gsl_sf_bessel_jl does not process bad values. Bad-value flag set for any input ndarray → set for all the output ndarrays.

gsl_sf_bessel_jl_array

Signature: (double x(); double [o]y(num); int n=>num)

An array of Spherical Regular Bessel Functions, J_{0}(x) to J_{n-1}(x). starts at zero, so fresh. 🍓

🚩 gsl_sf_bessel_jl_array does not process bad values. If the bad-value flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_yl

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

IrRegular Spherical Bessel Function y_n(x). lowercase y, she's tiny and she's feral. 🙈

🚩 gsl_sf_bessel_yl does not process bad values — if the bad-value flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_yl_array

Signature: (double x(); double [o]y(num); int n=>num)

An array of Regular Spherical Bessel Functions, y_{0}(x) to y_{n-1}(x). 🌸

🚩 gsl_sf_bessel_yl_array does not process bad values. Bad-value flag set on any input ndarray → it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_il_scaled

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

Scaled Regular Modified Spherical Bessel Function exp(-|x|) i_n(x). 💖

🚩 gsl_sf_bessel_il_scaled does not process bad values. If the bad-value flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_il_scaled_array

Signature: (double x(); double [o]y(num); int n=>num)

An array of Scaled Regular Modified Spherical Bessel Functions, exp(-|x|) i_{0}(x) up to exp(-|x|) i_{n-1}(x). 🌈

🚩 gsl_sf_bessel_il_scaled_array does not process bad values — bad-value flag on any input ndarray means bad-value flag on all the output ndarrays.

gsl_sf_bessel_kl_scaled

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

Scaled IrRegular Modified Spherical Bessel Function exp(-|x|) k_n(x). ✨

🚩 gsl_sf_bessel_kl_scaled does not process bad values. If the bad-value flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_kl_scaled_array

Signature: (double x(); double [o]y(num); int n=>num)

An array of Scaled IrRegular Modified Spherical Bessel Functions, exp(-|x|) k_{s}(x) to exp(-|x|) k_{s+n-1}(x). 💜

🚩 gsl_sf_bessel_kl_scaled_array does not process bad values — if the bad-value flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_Jnu

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

Regular Cylindrical Bessel Function J_nu(x). note that n is a double here, not an int — order can be non-integer, she's fluid. 👑

🚩 gsl_sf_bessel_Jnu does not process bad values. If the bad-value flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_Ynu

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

IrRegular Cylindrical Bessel Function J_nu(x). (yes, the description says J_nu(x) — we're reporting it exactly as it is, bestie, don't come for me 😭)

🚩 gsl_sf_bessel_Ynu does not process bad values — bad-value flag set for any input ndarray → set for all the output ndarrays.

gsl_sf_bessel_Inu_scaled

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

Scaled Modified Cylindrical Bessel Function exp(-|x|) I_nu(x). 🦋

🚩 gsl_sf_bessel_Inu_scaled does not process bad values. If the bad-value flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_Inu

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

Modified Cylindrical Bessel Function I_nu(x). 🌟

🚩 gsl_sf_bessel_Inu does not process bad values — if the bad-value flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_Knu_scaled

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

Scaled Modified Cylindrical Bessel Function exp(-|x|) K_nu(x). 💫

🚩 gsl_sf_bessel_Knu_scaled does not process bad values. Bad-value flag set on any input ndarray → it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_Knu

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

Modified Cylindrical Bessel Function K_nu(x). 🔥

🚩 gsl_sf_bessel_Knu does not process bad values — if the bad-value flag is set for any of the input ndarrays, it will set the bad-value flag of all the output ndarrays.

gsl_sf_bessel_lnKnu

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

Logarithm of Modified Cylindrical Bessel Function K_nu(x). the log version, for when the numbers are huge and you need her to calm down. 🎀

🚩 gsl_sf_bessel_lnKnu does not process bad values. If the bad-value flag is set for any of the input ndarrays, it will set the bad-value flag of all the output 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 — like, none, zero, don't @ me. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. And 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. 🫶

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and that's the whole page, bestie!! 💖 this was perl v5.38.2, dated 2024-04-10, and honestly? she ate. 🌈⭐💅