Question 14243. (Q1513703)
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scientific article; zbMATH DE number 2665435
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Question 14243. |
scientific article; zbMATH DE number 2665435 |
Statements
Question 14243. (English)
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1900
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Es seien \(p\) und \(m\) ganze Zahlen, \(p > m\), so ist für ungerades \(m\): \[ \int_0^\pi x\cos px\sin^mxdx = \frac{(-1)^{\frac12[m+(-1)^p]}\cdot m!\pi}{(p^2-1^2)(p^2-3^2)\dots(p^2-m^2)}, \] für gerades \(m\): \[ \int_0^\pi x\sin px\sin^mxdx = \frac{(-1)^{\frac12[m+(-1)^p]}\cdot m!\pi}{(p^2-2^2)(p^2-4^2)\dots(p^2-m^2)}. \] Beweis von J. H. Dipp.
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