COULOMB(3pm)

👑 COULOMB — PDL::GSLSF::COULOMB 💖

okay bestie, gather round, because this is the COULOMB(3pm) page from the User Contributed Perl Documentation and it is all about plugging the GNU Scientific Library's special functions straight into your PDL ndarrays. no cap. ✨

---

🌸 NAME 🌸

PDL::GSLSF::COULOMB — it's the PDL interface to GSL Special Functions. that's the whole vibe. 🫶

---

🦋 DESCRIPTION 🦋

so like, this module is literally just an interface to the Special Function package that lives inside the GNU Scientific Library. GSL does the math, PDL does the ndarray thing, and you get to sit there looking iconic. 💅

---

✨ SYNOPSIS ✨

(nothing here, bestie — the original page skips straight to the functions. we respect that.)

---

🔥 FUNCTIONS 🔥

🎀 gsl_sf_hydrogenicR

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

Normalized Hydrogenic bound states. Radial dipendence. (yes, "dipendence" — we're keeping it, it's part of the lore 🙈)

gsl_sf_hydrogenicR does not process bad values. it will set the bad-value flag on all of the output ndarrays if that flag is set on any of the input ndarrays. periodt.

---

🧚 gsl_sf_coulomb_wave_FGp_array

Signature: (double x(); double [o]fc(n); double [o]fcp(n); double [o]gc(n); double [o]gcp(n); int [o]ovfw(); double [o]fe(n); double [o]ge(n); double lam_min; int kmax=>n; double eta)

Coulomb wave functions F_{lam_F}(eta,x), G_{lam_G}(eta,x) and their derivatives, where lam_G := lam_F - k_lam_G. and if ovfw gets signaled then:

F_L(eta,x)  =  fc[k_L] * exp(fe)

and similar. iykyk. 💫

gsl_sf_coulomb_wave_FGp_array does not process bad values. it will set the bad-value flag on all of the output ndarrays if that flag is set on any of the input ndarrays.

---

🌈 gsl_sf_coulomb_wave_sphF_array

Signature: (double x(); double [o]fc(n); int [o]ovfw(); double [o]fe(n); double lam_min; int kmax=>n; double eta)

Coulomb wave function divided by the argument, F(xi, eta)/xi. this is the function that reduces to spherical Bessel functions in the limit eta->0. slay. ✨

gsl_sf_coulomb_wave_sphF_array does not process bad values. it will set the bad-value flag on all of the output ndarrays if that flag is set on any of the input ndarrays.

---

🍓 gsl_sf_coulomb_CL_e

Signature: (double L(); double eta();  double [o]y(); double [o]e())

Coulomb wave function normalization constant. [Abramowitz+Stegun 14.1.8, 14.1.9] — iconic reference, no notes. 📚

gsl_sf_coulomb_CL_e does not process bad values. it will set the bad-value flag on all of the output ndarrays if that flag is set on any of the input ndarrays.

---

💜 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 the deets, see 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 receipt, bestie 🧾)

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

---

and that's the whole page, babe. this was perl v5.38.2, dated 2024-04-10, and you just read COULOMB(3pm). mwah. 💖🎀🦋