The history of the integral \(\int_0^\infty \frac{\sin x}{x}\,dx\): a history of analysis in a nutshell (Q873920)
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scientific article; zbMATH DE number 5135828
| Language | Label | Description | Also known as |
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| English | The history of the integral \(\int_0^\infty \frac{\sin x}{x}\,dx\): a history of analysis in a nutshell |
scientific article; zbMATH DE number 5135828 |
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The history of the integral \(\int_0^\infty \frac{\sin x}{x}\,dx\): a history of analysis in a nutshell (English)
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20 March 2007
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What with its oscillating integrand and the infinite range of its variable, this integral was rather hard for the power of the theory of integration of the early 19th century. As the author suggests in the sub-title of his paper, it proved a formidable test case in the development of the evaluation of definite integrals from Euler through Laplace, Fourier, Poisson and Cauchy to a more critical phase featuring Dirichlet and Bonnet and then to assessments at the turn of the centuries by figures such as de la Vallée Poussin and Hardy.
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