Talk:Schwarz triangle function: Difference between revisions

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comments on hypergeometric ODE which was not discussed in the body of the article
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:Later that was modified when another editor inserted content about the hypergeometric ODE tight at the beginning of the lead. As a result crucial conditions on the Schwarz triangles were omitted (that the angles should have the form 0 or {{pi}} over a positive integer) and the geometric connection with tessellations was lost. It is probably a good idea to merge the first version of the lead with the additional content on the hypergeometric function. The densely written paragraph of my original lead can certainly be written in a way that makes it far more approachable to readers.
 
:Clearly the final section of the article was incomplete. Unfortunately on wikipedia that is often what happens. On the other hand, the theory of the hypergeometric ODE is easy to summarisedsummarise briefly with exact page references for the books of Caratheodory, Hille and Nehari (already listed in the article). The case of ideal triangles can also be briefly summarised from the 2nd edition of Ahlfors book on Complex Analysis, where the [[modular lambda function]] appears. In this way missing material and page numbers can be added, matching up content on the uniformization problem (conformal mapping of Schwarz triangles) and the hypergeometric ODE. [[User:Mathsci|Mathsci]] ([[User talk:Mathsci|talk]]) 00:43, 8 October 2021 (UTC)