On a formula for \(\pi_\nu(x)\). (Q2614375)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a formula for \(\pi_\nu(x)\). |
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On a formula for \(\pi_\nu(x)\). (English)
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1935
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Verf. beweist für die Anzahl \(\pi_\nu(x)\) der Zahlen \(\leqq x\), welche genau \(\nu\) verschiedene Primzahlen enthalten: \[ \pi_\nu(x)=\dfrac1{(\nu-1)!}\dfrac{x(\log\log x)^{\nu-1}}{\log x}+ \dfrac{B}{(\nu-2)!}\dfrac{x(\log\log x)^{\nu-2}}{\log x}+ o\bigg(\dfrac{x(\log\log x)^{\nu-2}}{\log x}\bigg). \] Dem Verf. scheint eine Arbeit von \textit{Landau} (Nachr. Ges. Wiss. Göttingen 1911, 361-381; F. d. M. 42, 221 (JFM 42.0221.*)) nicht bekannt zu sein, in der wesentlich früher ein wesentlich genaueres Resultat bewiesen worden ist.
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