Taylor series

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A Taylor series is a way to express a function as an infinite series under suitable differentiability conditions. The Taylor series is typically given by $$f(x) = \displaystyle\sum_{k=0}^{\infty} f^{(k)}(x_0) (x-x_0)^k,$$ where $(k)$ denotes differentiation.

Examples of Taylor series[edit]

Taylor series of the exponential function
Taylor series of sine
Taylor series of cosine
Taylor series for sinh