Borel's lemma
= Borel's lemma
{wiki=Borel's_lemma}
Borel's lemma is a result in the theory of functions, particularly in the context of real or complex analysis. It states the following: Let \\( f \\) be a function defined on an open interval \\( I \\subseteq \\mathbb\{R\} \\) that is infinitely differentiable (i.e., \\( f \\in C^\\infty(I) \\)). If \\( f \\) and all of its derivatives vanish at a point \\( a \\in I \\) (i.e.