borel in A Sentence

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    By Borel's lemma, f can be extended to a smooth function on the whole of Rn.

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    Félix Édouard Justin Émile Borel(French:; 7 January 1871- 3 February 1956) was a French mathematician and politician.

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    All of these methods are strictly weaker than Borel summation; for q > 0 they are incomparable with Abel summation.

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    This is similar to Borel's integral summation method, except that the Borel transform need not converge for all t, but converges to an analytic function of t near 0 that can be analytically continued along the positive real axis.

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    5

    The Borel sum of 1- 2 + 4- 8 + ⋯ is also 1/3; when Émile Borel introduced the limit formulation of Borel summation in 1896, this was one of his first examples after 1- 1 + 1- 1 + ⋯ Leibniz pp. 205-207 Knobloch pp.

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