A power series satisfying a certain functional equation (Q5954667)
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scientific article; zbMATH DE number 1701646
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A power series satisfying a certain functional equation |
scientific article; zbMATH DE number 1701646 |
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A power series satisfying a certain functional equation (English)
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10 September 2002
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On hand of structural formulas for some chemical substances, the authors offer upper and lower estimates for the radii of convergence of power series \(f\) and \(g\) that satisfy the functional equations \(f(z)=1+z[f(z)^2 +f(z^2)]/2\) or \(g(z)=1+z[g(z)^3 +3g(z)g(z^2)+2g(z^3)]/6,\) respectively, the latter being better than those presented by \textit{G. Pólya} [Acta Math. 68, 145-254 (1937; Zbl 0017.23202)]. Transcendency results follow concerning the function defined by \(f.\)
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functional equations
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power series
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radius of convergence
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