Definition:Du Bois-Reymond Constants
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Definition
The du Bois-Reymond constants are the constants $C_n$ where:
- $C_n = \ds \int_0^\infty \size {\map {\dfrac \d {\d t} } {\dfrac {\sin t} t}^n} \rd t - 1$
Examples
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:
\(\ds C_2\) | \(=\) | \(\ds \dfrac {e^2 - 7} 2\) | ||||||||||||
\(\ds \) | \(\approx\) | \(\ds 0 \cdotp 19452 \, 80494 \, 6532 \ldots\) |
Source of Name
This entry was named for Paul David Gustav du Bois-Reymond.
Sources
- 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $0,19452 80494 6532 \ldots$
- Weisstein, Eric W. "du Bois-Reymond Constants." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/duBois-ReymondConstants.html