Funções Trigonométricas e Hiperbólicas de Terceira Ordem

Talison  Gomes Moreira; José Eloy Ottoni; Amanda Ottoni

Talison Gomes Moreira Universidade Federal de São João del-Rei
José Eloy Ottoni Universidade Federal de São João del-Rei https://orcid.org/0000-0002-0074-243X
Amanda Ottoni Universidade Federal de São João del-Rei https://orcid.org/0000-0002-7797-6760

Palavras-chave: Funções hiperbólicas generalizadas, Funções hiperbólicas de terceira ordem, Funções 8 trigonométricas de terceira ordem

Resumo

Este trabalho tem como objetivo apresentar as funções trigonométricas e hiperbólicas generalizadas, mais especificamente as funções trigonométricas e hiperbólicas de terceira ordem, bem como a relação entre elas, seus gráficos, suas derivadas e alguma menção à sua história e algumas aplicações.

Referências

[1] Aguiar, Luiz Bizerra de. Relações complexas entre as funções hiperbólicas e a transmissão de energia. Revista Científico, 18(37):189–206, 2018.
[2] Appell, P. Sur certaines fonctions analogues aux fonctions circulaires. CR Acad. Sci. Paris, 84:1378–1380, 1877.
[3] Appell, P. Propositions d’algèbre et de géométrie déduites de la considération des racines cubiques de l’unité. Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris, 84:540–543, 1877.
[4] Bell, E. T. A laplacian equation. The American Mathematical Monthly, 39(9):515– 517, 1932. DOI: 10.2307/2300825.
[5] Davis, Philip J. Circulant matrices. Chelsea Pub Co; 2ª edição. ISBN-10: 0821891650, ISBN-13: 978-0821891650, 2012.
[6] Devisme, Jacques. Sur l’équation de m. pierre humbert. In Annales de la Faculté des sciences de Toulouse: Mathématiques, volume 25, pages 143–238, 1933. Zbl0009.16803.
[7] Filho, Edson Pereira Arruda. As elegantes matrizes circulantes. Master’s thesis, 2019. PROFMAT-UFSJ.
[8] Free Software Foundation. Geogebra. https://www.geogebra.org.
[9] Good, I. J. Skew circulants and the theory of numbers. The Fibonacci Quarterly, 24(2):47–60, 1986.
[10] Gray, Robert M. Toeplitz and circulant matrices: A review. Communications and Information Theory, 2(3):155––239, 2006. DOI: 10.1561/0100000006.
[11] Jagannathan, Ramaswamy. On generalized clifford algebras and their physical applications. In The legacy of Alladi Ramakrishnan in the mathematical sciences, pages 465–489. Springer, 2010.
[12] Kaufman, H. A generalization of the sine function. The American Mathematical Monthly, Mathematical Notes, 64(3):181–183, 1957. DOI: 10.2307/2310551.
[13] Kittappa, R. K. A generalization of the rotation matrix and related results. Linear Algebra and its Applications, 92:251–258, 1987. DOI: 10.1016/0024-3795(87)90262-X.
[14] Kwasniewski, A. K. A note on generalized rademacher and hyperbolic functions. In Clifford Algebras and their Applications in Mathematical Physics, pages 215–219. Springer, 1992.
[15] MacHale, Desmond. My favourite polynomial. The Mathematical Gazette, 75(472):157–165, 1991. DOI: 10.2307/3620243.
[16] Mingoranci, Marcos Rogério. Uma introdução à trigonometria hiperbólica e sua aplicação no ensino médio. Master’s thesis, 2016. PROFMAT - UFMS.
[17] Moreira, Talison Gomes. Um estudo sobre funções trigonométricas e hiperbólicas de terceira ordem. Master’s thesis, 2020. PROFMAT - UFSJ.
[18] Morinaga, Kakutaro and N ¯ ono, Takayuki and others. On the linearization of a ¯ form of higher degree and its representation. Journal of Science of the Hiroshima University, Series A (Mathematics, Physics, Chemistry), 16:13–41, 1952. DOI: 10.32917/hmj/1557367250.
[19] Muldoon, Martin E. Generalized hyperbolic functions, circulant matrices and functional equations. Linear algebra and its applications, 406:272–284, 2005. DOI: 10.1016/J.LAA.2005.04.011.
[20] Muldoon, Martin E. and Ungar, Abraham A. Beyond sin and cos. Mathematics Magazine, 69(1):3–14, 1996. DOI: 10.1080/0025570X.1996.11996374.
[21] Oniga, Théodore. Analyse mathematique-sur une generalisation des fonctions circulaires et hyperboliques. Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris, 227(22):540, 1948.
[22] Ramakrishnan, Alladi. A new approach to internal quantum numbers. In Procee344 dings of the Conference on Clifford Algebra, Its Generalization and Applications, pages 87–96. Matscience, 1971.
[23] Silberstein, Ludwjk. Differentially cyclical sets of functions. an extension of the concept of hyperbolic functions. The London, Edinburgh, and Du348 blin Philosophical Magazine and Journal of Science, 33(221):457–461, 1942. DOI:10.1080/14786444208521211.
[24] Ungar, Abraham. Generalized hyperbolic functions. The American Mathematical Monthly, 89(9):688–691, 1982. DOI: 10.1080/00029890.1982.11995514,.
[25] Ungar, Abraham. Higher order alpha-hyperbolic functions. Indian J. pure appl. Math, 15(3):301–304, 1984.
[26] Villarino, Mark B. A cubic surface of revolution. The Mathematical Gazette, 98(542):281–290, 2015. DOI: 10.1017/S0025557200001327.
[27] Ward, L. E. Some functions analogous to trigonometric functions. The American Mathematical Monthly., 34(6):301–303, 1927. DOI: 10.1080/00029890.1927.11986709,.