EXPINT(3pm)

💖 EXPINT — PDL::GSLSF::EXPINT 💖

okay so bestie, this is the EXPINT(3pm) page, and it lives in the User Contributed Perl Documentation section. yes we're doing math today. yes it's giving main character energy. come on. 🧚✨

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🌸 NAME 🌸

PDL::GSLSF::EXPINT — it's the PDL interface to GSL Special Functions. no cap, that's the whole name, she's lowkey modest about it 💅

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✨ DESCRIPTION ✨

So basically: this is an interface to the Special Function package present in the GNU Scientific Library. that's it. that's the description. the GSL said "here's my special functions" and PDL said "say less bestie, I'll wrap them" 🫶

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👑 FUNCTIONS 👑

Nine functions. All of them. We are NOT skipping any, I don't care how tired you are, we're going through all of them together like the icons we are 💖

Every single one of these has the same signature vibe:

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

and every single one of them does not process bad values. Which means — listen up, this part is real — it will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. Like, one bad input and the whole output situation is flagged. the drama is real 😭

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🦋 gsl_sf_expint_E1 🦋

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

E_1(x) := Re[ Integrate[ Exp[-xt]/t, {t,1,Infinity}] ]

• gsl_sf_expint_E1 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_expint_E2 🦋

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

E_2(x) := Re[ Integrate[ Exp[-xt]/t^2, {t,1,Infity}] ]

• gsl_sf_expint_E2 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.

(yes it says Infity in the original and no I will not be correcting it, that's her little typo, we respect her 🎀)

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🦋 gsl_sf_expint_Ei 🦋

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

Ei(x) := PV Integrate[ Exp[-t]/t, {t,-x,Infinity}]

• gsl_sf_expint_Ei 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_Shi 🦋

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

Shi(x) := Integrate[ Sinh[t]/t, {t,0,x}]

• gsl_sf_Shi 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_Chi 🦋

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

Chi(x) := Re[ M_EULER + log(x) + Integrate[(Cosh[t]-1)/t, {t,0,x}] ]

• gsl_sf_Chi 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_expint_3 🦋

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

Ei_3(x) := Integral[ Exp[-t^3], {t,0,x}]

• gsl_sf_expint_3 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_Si 🦋

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

Si(x) := Integrate[ Sin[t]/t, {t,0,x}]

• gsl_sf_Si 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_Ci 🦋

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

Ci(x) := -Integrate[ Cos[t]/t, {t,x,Infinity}]

• gsl_sf_Ci 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_atanint 🦋

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

AtanInt(x) := Integral[ Arctan[t]/t, {t,0,x}]

• gsl_sf_atanint 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 🎀

Okay so, the receipts, because we always credit people:

This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it>. All rights reserved. There is no warranty — like, none, zero, nada, do not come for her if your math breaks 😭. 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. periodt 💅

The GSL SF modules were written by G. Jungman. iconic behaviour honestly 👑

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and that's the whole page bestie!! every function, every signature, every bad-value warning, every formula, exactly as she wrote it. ate and left no crumbs 🍓✨

this was perl v5.38.2, dated 2024-04-10, and the page is EXPINT(3pm) — mwah, love u, go integrate something 💖🦋🎀