Everything about Schwarz triangle function
Conformal mappings in complex analysis
In complex analysis, the Schwarz triangle function or Schwarz s-function is a function that 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 is the most mathematically interesting case. When that triangle is a non-overlapping Schwarz triangle, i.e. a Möbius triangle, the inverse of the Schwarz triangle function is a single-valued automorphic function for that triangle's triangle group. More specifically, it is a modular function. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Schwarz triangle functionA 5-minute orientation
- Pick up a classic book: The non-Plessner points for the Schwarz triangle functionsThe most-reprinted book on the subject
- Read the landmark paper: Note on the Schwarz triangle functionsCited 6 times
- Go sideways: Schwarz–Christoffel mappingA closely related topic
- Go sideways: Hypergeometric functionA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
đź“š Books worth reading
- 📕The non-Plessner points for the Schwarz triangle functionsPaul M. Gauthier · 1968
Al-JabrHatem Al-Ani, Ali Al-Ani · 2026
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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