On the expression for the product of any two Legendre's coefficients by means of a series of Legendre's coefficients. (Q1553432)
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scientific article; zbMATH DE number 2711221
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the expression for the product of any two Legendre's coefficients by means of a series of Legendre's coefficients. |
scientific article; zbMATH DE number 2711221 |
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On the expression for the product of any two Legendre's coefficients by means of a series of Legendre's coefficients. (English)
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1878
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Der Verfasser hat früher (Febr. 1873) den Satz gefunden: \[ \int_{-1}^1P_mP_nP_pdp =\frac1{s+\frac12} \frac{A(s-m)A(s-n)A(s-p)}{A(s)}, \] wo \[ s=\frac12(m+n+p) \quad \text{und}\quad A(m)=2^m\cdot \frac{\frac12\cdot \frac32\cdot m-\frac12}{1\cdot2\cdots m} \] \[ =2^m\cdot \frac{\varPi(m-\frac12)}{\varPi(m)\varPi(-\frac12)}. \] Der Satz wurde unabhängig auch 1874 von Herrn Ferrers entdeckt und ist in seinen ``Spherical harmonics'' London 1877 publicirt.
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spherical harmonics
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