On the periodicity of trigonometric functions generalized to quotient rings of R[x] |
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Authors: | Claude Gauthier |
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Affiliation: | (1) Department of Mathematics and Statistics, Université de Moncton, Moncton, N.B., Canada |
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Abstract: | We apply a method of Euler to algebraic extensions of sets of numbers with compound additive inverse which can be seen as quotient rings of R[x]. This allows us to evaluate a generalization of Riemann’s zeta function in terms of the period of a function which generalizes the function sin z. It follows that the functions generalizing the trigonometric functions on these sets of numbers are not periodic. |
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Keywords: | Compound inverse generalized trigonometric functions zeta function |
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