Du Bois-Reymond Constants/Examples

From ProofWiki
Jump to navigation Jump to search

Examples of Du Bois-Reymond Constants

First 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.

Second du Bois-Reymond Constant

The second du Bois-Reymond constant $C_2$ evaluates as:

\(\displaystyle C_2\) \(=\) \(\displaystyle \dfrac {e^2 - 7} 2\)
\(\displaystyle \) \(\approx\) \(\displaystyle 0 \cdotp 19452 \, 80494 \, 6532 \ldots\)