Theorems stated by Ramanujan. V: Approximations connected with \(e^x\). (Q1835389)
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scientific article; zbMATH DE number 2570021
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Theorems stated by Ramanujan. V: Approximations connected with \(e^x\). |
scientific article; zbMATH DE number 2570021 |
Statements
Theorems stated by Ramanujan. V: Approximations connected with \(e^x\). (English)
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1929
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\textit{Ramanujan} hat bewiesen (Collected papers, 24): In \[ 1 + \frac{x}{1!} + \frac{x^2}{2!} + \ldots + \frac{x^x}{x!}y = \frac{e^x}{2} \, \text{ist} \] \[ y = \frac{1}{3} + \frac{4}{135(x+k)} \] mit \[ \frac{8}{45} \geq k \geq \frac{2}{21}. \] Verf. untersucht mit Hilfe von Integraldarstellungen für \(y\) das Verhalten von \(k\) näher und gibt Tabellen für einige damit zusammenhängende Größen.
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