Difference between revisions of "Buchstab function"
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The Buchstab function is a [[continuous]] function $\omega \colon [1,\infty) \rightarrow (0,\infty)$ defined by the [[initial value problem]] | The Buchstab function is a [[continuous]] function $\omega \colon [1,\infty) \rightarrow (0,\infty)$ defined by the [[initial value problem]] | ||
| − | $$\dfrac{d}{ | + | $$\dfrac{\mathrm{d}}{\mathrm{d}u}\Big(u\omega(u-1)\Big); u \geq 2$$ |
| − | and for $1 \leq u \ | + | and for $1 \leq u \leq 2$, $\omega(u)=\dfrac{1}{u}$. |
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| + | =References= | ||
| + | [http://www.ams.org/journals/mcom/1990-55-191/S0025-5718-1990-1023043-8/S0025-5718-1990-1023043-8.pdf A differential delay equation arising from the Sieve of Eratosthenes] | ||
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| + | [[Category:SpecialFunction]] | ||
Latest revision as of 13:32, 8 November 2024
The Buchstab function is a continuous function $\omega \colon [1,\infty) \rightarrow (0,\infty)$ defined by the initial value problem $$\dfrac{\mathrm{d}}{\mathrm{d}u}\Big(u\omega(u-1)\Big); u \geq 2$$ and for $1 \leq u \leq 2$, $\omega(u)=\dfrac{1}{u}$.
References
A differential delay equation arising from the Sieve of Eratosthenes
