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Bemerkung zu Herrn Stridsbergs Beweis des Waringschen Theorems. (German) JFM 43.0238.03

Siehe F. d. M. 41, 224 (JFM 41.0224.*), 1910; Stridsberg schließt durch Einführung des Symboles \(h\) aus \[ h^{2\mu}=\dfrac{(2\mu)!}{\mu!}=\dfrac{1}{\varGamma\bigl(\frac12\bigr)} \int\limits_{-\infty}^{+\infty}e^{-\tfrac{\alpha^2}{4}}\alpha^{2\mu}\,d\alpha, \;\;\;f(h)=\dfrac{1}{\varGamma \bigl(\frac12\bigr)}\int\limits^{+\infty}_{-\infty} e^{-\tfrac{\alpha^2}{4}}f(\alpha)\,d\alpha, \] sofort, daß, wenn \(f(\alpha)\geqq 0\) für alle reellen \(\alpha\) und \(f(\alpha) \not \equiv 0\), auch \(f(h) >0\).
Der Verf. gibt für letztere Aussage einen elementaren Beweis, der die Integralrechnung nicht benutzt.

Citations:

JFM 41.0224.*
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References:

[1] Math. Ann. 67 (1909), S. 281. · JFM 40.0095.03
[2] Ibid Math. Ann. 67 (1909), S. 301.
[3] Arkiv för Mat., Astr. Fys. 6, Nr. 32, 39.
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