A note on a problem concerning \textit{Dirichlet} integrals. (Q1470607)
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scientific article; zbMATH DE number 2610762
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on a problem concerning \textit{Dirichlet} integrals. |
scientific article; zbMATH DE number 2610762 |
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A note on a problem concerning \textit{Dirichlet} integrals. (English)
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1916
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Der Mittelwert von \(x_1^{2m}+x_2^{2m}+\dots+x_n^{2m}\) in der durch \[ x_1^2+x_2^2+\cdots+x_n^2\leqq R^2,\;x_1+x_2+\cdots+x_n=0 \] charakterisierten \((n-1)\)-dimensionalen Kugel ist \[ n\left(\frac{n-1}{n}\right)^m \frac{1\cdot 3\cdot 5\cdots (2m- 1)}{(n+1)(n+3)(n+5)\cdots(n+2m-1)}R^{2m} \] und einige analoge Resultate.
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