Higher Trigonometry: A Class Of Nonlinear Systems

2019/07/10 by P. L. Robinson, Robinson, P. L.
Mathematics · #34A34 #34M05 #Advanced Combinatorial Mathematics #Advanced Mathematical Theories #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematics and Applications #math.CA #msc:34A34 #msc:34M05

paper · pdf · doi:10.48550/arxiv.1907.05240

arxiv created 2019/07/10 · openalex publication_date 2019/07/10 · arxiv updated 2019/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the initial value problem 's ' = c^{p - 1}, c ' = -s^{p - 1}; s(0) = 0, c(0) = 1' (both as a real system and as a complex system) for each integer p > 2, considering separately the cases 'p even' and 'p odd'.

Citations

• The Dixonian elliptic functions
• Meromorphic functions in a first-order system

Related

• Nearly cosine series and generalized trigonometric functions
• Trigonometric functions in the p-norm
• A tangential approach to trigonometry
• A remark on the trigonometric system
• Improved q-exponential and q-trigonometric functions