AppellF1

Generated from the engine's own definition: compute-engine's symbol, which we neither extend nor document by hand.

Appell hypergeometric function F₁(a; b₁, b₂; c; x, y), double series for |x|, |y| < 1.

WikipediaAppell series↗WikidataQ4780998↗

AppellF1(complex | infinity, complex | infinity, complex | infinity, complex | infinity, complex | infinity, complex | infinity) -> numberas compute-engine declares it

mpmathappellf1(complex | infinity, complex | infinity, complex | infinity, complex | infinity, complex | infinity, complex | infinity)

Typed signatures

Type	Package	Applies
(complex | infinity, complex | infinity, complex | infinity, complex | infinity, complex | infinity, complex | infinity) -> number	compute-engine	always

Domain: Compute engine

Plot

the complex plot cannot lower AppellF1

Examples

Basic #

Every Appell series is $1$ at the origin

live ↗

In$\mathrm{AppellF1}(1, 1, 1, 2, 0, 0)$Out$1$

live ↗

In$N(\mathrm{AppellF1}(1, 1, 1, 2, 0.1, 0.2), 15)$Out$1.177\,830\,356\,563\,83$

Known value · mpmath 1.3.0 appellf1

About

Examples	2
Checked against	mpmath 2 agree
Crosswalk	WikipediaWikidatampmath

Implementation

mappedmpmathpackages/oracle/src/mappings.ts