Peano's Unnoticed Proof of Borel's Theorem
نویسنده
چکیده
In 1876, P. du Bois-Reymond gave an example of an infinitely differentiable function whose Taylor series diverges everywhere except one point. By generalizing this example, G. Peano proved a theorem in 1884, often credited to É. Borel, which states that every power series is a Taylor series of some infinitely differentiable function. The aim of the paper is to recall Peano’s unnoticed contributions to this result.
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عنوان ژورنال:
- The American Mathematical Monthly
دوره 121 شماره
صفحات -
تاریخ انتشار 2014