Expanding the function \(\ln(1 + \operatorname{e}^x)\) into power series in terms of the Dirichlet eta function and the Stirling numbers of the second kind (Q6589510)
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scientific article; zbMATH DE number 7898637
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Expanding the function \(\ln(1 + \operatorname{e}^x)\) into power series in terms of the Dirichlet eta function and the Stirling numbers of the second kind |
scientific article; zbMATH DE number 7898637 |
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Expanding the function \(\ln(1 + \operatorname{e}^x)\) into power series in terms of the Dirichlet eta function and the Stirling numbers of the second kind (English)
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19 August 2024
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The authors provide several simple and alternative proofs of the conjecture proposed by G. Helms in the year 2013. They expand the composite function into power series whose coefficients are expressed in terms of the Dirichlet eta function and the Stirling numbers of the second kind.
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Dirichlet eta function
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composite function
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power series expansion
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Stirling number of second kind
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Riemann zeta function
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partial Bell polynomial
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