Proof of Rodrigues' theorem. (Q5914681)
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scientific article; zbMATH DE number 2709538
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Proof of Rodrigues' theorem. |
scientific article; zbMATH DE number 2709538 |
Statements
Proof of Rodrigues' theorem. (English)
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1880
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Rodrigues' Satz lautet: \[ \frac 1{(n-m)!} \frac {d^{n-m}}{dx^{n-m}} (x^2-1)^n = (x^2-1)^m \frac 1{(n+m)!} \frac {d^{n+m}}{dx^{n+m}} (x^2-1)^m . \] Des Verfassers Beweis beruht auf der Betrachtung der Coefficienten von \(h^{n-m}\) und \(h^{n+m}\) in dem Product \[ (x-1+h)^n (x+1+h)^m . \]
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Differential and integral calculus
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