AGM

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

Arithmetic-geometric mean. AGM(z) is shorthand for AGM(1, z) (Fungrim convention).

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaArithmetic–geometric mean↗MathWorldArithmetic-GeometricMean↗WikidataQ476167↗DLMF19.8.i.p1↗FungrimAGM✓↗Fungrim entry

AGM(complex | infinity, (complex | infinity)?) -> numberAs native, and keeps its digits past a double's off the positive reals (N(AGM(1, -10), 20)).

Typed signatures

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

Domain: Compute engine

Plot

ComplexPlot

real slice

Examples

5 more kept as data, checked against the oracles

Basic #

The mean of $1$ and $2$, to 20 digits

live ↗

In$N(\mathrm{AGM}(1, 2), 20)$Out$1.456\,791\,031\,046\,906\,869\,2$

Known value · mpmath 1.3.0 agm

Complex arguments #

The mean of $1$ and $-10$ to 20 digits: on the cut along the negative reals, the limit from above it

live ↗

In$N(\mathrm{AGM}(1, -10), 20)$Out$-2.462\,181\,891\,100\,572\,793\,6+2.098\,317\,353\,043\,635\,162\,9i$

Known value · Wolfram 15 ArithmeticGeometricMean

About

Examples	7
Checked against	Wolfram Language 7 agreempmath 3 agree4 differJulia 5 agree2 differ
Crosswalk	WikipediaMathWorldWikidataDLMFFungrimFungrim entry ×27mpmathJulia

Implementation

mappedwolframpackages/oracle/src/mappings.ts

mappedmpmathpackages/oracle/src/mappings.ts

mappedjuliapackages/oracle/src/mappings.ts