Solution of the equation \(f'(x)=f(1/x)\). (Q2586887)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solution of the equation \(f'(x)=f(1/x)\). |
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Solution of the equation \(f'(x)=f(1/x)\). (English)
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1940
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Verf. ist entgangen, daß aus der Gleichung (1) \(f'(x) = f\biggl(\dfrac1x\biggr)\) folgt (2) \(x^2 \cdot f''(x) + f (x) = 0\). Die Lösung von (1) lautet daher in reeller Form \[ f(x)=\dfrac{2}{\sqrt 3}f(1)\cdot \sqrt x \cos \biggl(\dfrac{\sqrt 3}{2}\log x-\dfrac\pi6\biggr). \]
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