A type of generalized trigonometric functions and some non-interesting applications

Han Yu

Frank Adams 2,

Trigonometric functions  e.g. \(sin\), \(cos\)...are very interesting, simple and full of magic. If we consider them as a pair of functions derived from the exponential function in a certain way, it is then not very un-natural to generalized the idea further, this will give us triple,quadruple, 5-ple...functions, those functions are less interesting, less simple, and not that full of magic but still, there will be applications such as evaluate series \(\sum_{i=0}^{\infty} \frac{n^k}{n^{2m}+1}\) and \(\sum_{i=0}^{\infty} \frac{n^k}{n^{2m}+1}\) for quite a lot of numbers \(k\) and \(m\). In the seminar, the construction of generalized trigonometric functions and the evaluation of the series will be talked about.

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