Du Bois-Reymond Constants/Example/First

Example of Du Bois-Reymond Constant

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

This is because:

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

does not converge for $n = 1$.

Proof

This theorem requires a proof. In particular: You can improve the proof in the sandbox: User:Sandbox/Du Bois-Reymond Constants/Example/First You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.