Schwarz triangle function: Difference between revisions

Revision as of 03:08, 17 August 2022

Revision as of 01:10, 18 August 2022

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{{short description|Conformal mappings in complex analysis}}

<noinclude>{{User:RMCD bot/subject notice|1=Schwarz triangle function|2=Talk:Schwarz triangle tessellation#Requested move 15 August 2022}}

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[[File:Schwarz triangle function.svg|thumb|PlotsThe ofupper half-plane, and the Schwarzimage triangleof functionthe forupper varioushalf-plane parameters,transformed transformingby the upperSchwarz halftriangle planefunction with various parameters.]]

{{Complex analysis sidebar}}

Upper left: Untransformed upper half-plane (grey) with gridlines.

Upper right: α = 1/2, β = 1/3, γ = 1/4.

Bottom left: α = β = γ = 1/3.

Bottom right: α = 1/5, β = 1/4, γ = 1/3.]]

In [[complex analysis]], the '''Schwarz triangle function''' or '''Schwarz s-function''' is a function that [[conformal mapping|conformally maps]] the [[upper half plane]] to a triangle in the upper half plane having lines or circular arcs for edges. The target triangle is not necessarily a [[Schwarz triangle]], although that case is the most mathematically interesting.