On the solution to a complicated functional equation (Q761553)
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scientific article; zbMATH DE number 3886175
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the solution to a complicated functional equation |
scientific article; zbMATH DE number 3886175 |
Statements
On the solution to a complicated functional equation (English)
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1983
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Es wird die Gleichung \[ -K= \ln x+\sum^{\infty}_{n=1}(-1)^{n-1}x^ n/n!\quad (mit\quad K>0) \] nach x aufgelöst. Resultat: \[ x=e^{-2K}- 2e^{-4K}+7e^{-6K}-(89/3)e^{-8K}+(557/4)e^{-10K}-+...\quad. \] Dabei wird die bekannte Methode der Reihenumkehrung verwendet, mit der eine Potenzreihe \(y=a_ 1x+a_ 2x^ 2+...\) \((a_ 1\neq 0)\) in eine Reihe \(x=b_ 1y+b_ 2y^ 2+...\) verwandelt wird.
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polynomial series
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special transcendental equation
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