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Is there are function to represent $x\mapsto\frac{\cos x}{x}$ as there is for $\sin x$, namely $\frac{\sin x}{x}=\text{sinc }x$?

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1 Answer

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The motivation for functions such as $\text{sinc}x,\,\text{sinch}x,\,\text{tanc}x,\,\text{tanch}x$ is to consider the behaviour of a ratio with limit $1$ as $x\to 0$. There is no such motivation for $\frac{\cos x}{x}$, since $\cos0 =1\ne 0$. However, you can write this ratio as $-\text{Ci}' \left( x\right)$.

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