In mathematics, Hadamard's lemma, named after Jacques Hadamard, is essentially a first-order form of Taylor's theorem, in which we can express a smooth, real-valued function exactly in a convenient manner.
Statement
Proof
Consequences and applications
See also Bump function – Smooth and compactly supported function Continuously differentiable – Degree of differentiability of a function or mapPages displaying short descriptions of redirect targets Smoothness – Degree of differentiability of a function or map Taylor's theorem – Approximation of a function by a polynomial
Citations
References Nestruev, Jet (2002). Smooth manifolds and observables. Berlin: Springer. ISBN 0-387-95543-7. Nestruev, Jet (10 September 2020). Smooth Manifolds and Observables. Graduate Texts in Mathematics. Vol. 220. Cham, Switzerland: Springer Nature. ISBN 978-3-030-45649-8. OCLC 1195920718.