ELLINT(3pm)

💜 ELLINT(3pm) — PDL::GSLSF::ELLINT 💜

okay bestie, gather round — this is a page from the User Contributed Perl Documentation section, and it's all about elliptic integrals living inside PDL. Let's go. 🎀

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✨ NAME ✨

PDL::GSLSF::ELLINT — the PDL interface to GSL Special Functions. yes queen, that's the whole vibe 🦋

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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 description. Short, sweet, iconic. 💅

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👑 FUNCTIONS 👑

heads up bestie: every single one of these functions has the exact same bad-value energy, so I'm gonna say it once per function anyway because the original does and we don't skip. Periodt. 💀

🧚 gsl_sf_ellint_Kcomp

Signature:

(double k(); double [o]y(); double [o]e())

Legendre form of complete elliptic integrals

K(k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}]

gsl_sf_ellint_Kcomp does not process bad values. It will set the bad-value flag on all output ndarrays if the flag is set for any of the input ndarrays. 🫶

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🌈 gsl_sf_ellint_Ecomp

Signature:

(double k(); double [o]y(); double [o]e())

Legendre form of complete elliptic integrals

E(k) = Integral[  Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}]

gsl_sf_ellint_Ecomp does not process bad values. It will set the bad-value flag on all output ndarrays if the flag is set for any of the input ndarrays. ✨

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💖 gsl_sf_ellint_F

Signature:

(double phi(); double k(); double [o]y(); double [o]e())

Legendre form of incomplete elliptic integrals

F(phi,k)   = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]

gsl_sf_ellint_F does not process bad values. It will set the bad-value flag on all output ndarrays if the flag is set for any of the input ndarrays. 🌸

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🦋 gsl_sf_ellint_E

Signature:

(double phi(); double k(); double [o]y(); double [o]e())

Legendre form of incomplete elliptic integrals

E(phi,k)   = Integral[ Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]

gsl_sf_ellint_E does not process bad values. It will set the bad-value flag on all output ndarrays if the flag is set for any of the input ndarrays. 💜

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🎀 gsl_sf_ellint_P

Signature:

(double phi(); double k(); double n();
 double [o]y(); double [o]e())

Legendre form of incomplete elliptic integrals

P(phi,k,n) = Integral[(1 + n Sin[t]^2)^(-1)/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]

gsl_sf_ellint_P does not process bad values. It will set the bad-value flag on all output ndarrays if the flag is set for any of the input ndarrays. 🍓

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⭐ gsl_sf_ellint_D

Signature:

(double phi(); double k();
 double [o]y(); double [o]e())

Legendre form of incomplete elliptic integrals

D(phi,k)

gsl_sf_ellint_D does not process bad values. It will set the bad-value flag on all output ndarrays if the flag is set for any of the input ndarrays. 🙈

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🔥 gsl_sf_ellint_RC

Signature:

(double x(); double yy(); double [o]y(); double [o]e())

Carlsons symmetric basis of functions

RC(x,y)   = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1)], {t,0,Inf}

gsl_sf_ellint_RC does not process bad values. It will set the bad-value flag on all output ndarrays if the flag is set for any of the input ndarrays. 🧚

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💀 gsl_sf_ellint_RD

Signature:

(double x(); double yy(); double z(); double [o]y(); double [o]e())

Carlsons symmetric basis of functions

RD(x,y,z) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-3/2), {t,0,Inf}]

gsl_sf_ellint_RD does not process bad values. It will set the bad-value flag on all output ndarrays if the flag is set for any of the input ndarrays. 👑

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🌟 gsl_sf_ellint_RF

Signature:

(double x(); double yy(); double z(); double [o]y(); double [o]e())

Carlsons symmetric basis of functions

RF(x,y,z) = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2), {t,0,Inf}]

gsl_sf_ellint_RF does not process bad values. It will set the bad-value flag on all output ndarrays if the flag is set for any of the input ndarrays. 🌈

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🫶 gsl_sf_ellint_RJ

Signature:

(double x(); double yy(); double z(); double p(); double [o]y(); double [o]e())

Carlsons symmetric basis of functions

RJ(x,y,z,p) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2) (t+p)^(-1), {t,0,Inf}]

gsl_sf_ellint_RJ does not process bad values. It will set the bad-value flag on 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>, 2002 Christian Soeller. 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. 🧚

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and that's the whole page, bestie — you ate that ✨

This lil masterpiece shipped with perl v5.38.2, dated 2024-04-10. 🎀 mwah, slay, bye 💅