Du Bois-Reymond Constants/Example/First

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Example of Du Bois-Reymond Constant

The first du Bois-Reymond constant $C_1$ does not exist.

This is because:

$\displaystyle \int_0^\infty \size {\map {\dfrac \d {\d t} } {\dfrac {\sin t} t}^n} \rd t - 1$

does not converge.


Proof