Hadamard's lemma
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In mathematics, Hadamard's lemma, named after
Jacques Hadamard Jacques Salomon Hadamard (; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry and partial differential equations. Biography The son of a teac ...
, is essentially a first-order form of
Taylor's theorem In calculus, Taylor's theorem gives an approximation of a ''k''-times differentiable function around a given point by a polynomial of degree ''k'', called the ''k''th-order Taylor polynomial. For a smooth function, the Taylor polynomial is th ...
, in which we can express a smooth, real-valued function exactly in a convenient manner.


Statement


Proof


Consequences and applications


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References

* * Real analysis Theorems in analysis