Du Bois-Reymond Constants/Examples
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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:
- $\ds \int_0^\infty \size {\map {\dfrac \d {\d t} } {\dfrac {\sin t} t}^n} \rd t - 1$
does not converge for $n = 1$.
Second du Bois-Reymond Constant
The second du Bois-Reymond constant $C_2$ evaluates as:
\(\ds C_2\) | \(=\) | \(\ds \dfrac {e^2 - 7} 2\) | ||||||||||||
\(\ds \) | \(\approx\) | \(\ds 0 \cdotp 19452 \, 80494 \, 6532 \ldots\) |