Revision #331 → #1619 · back to history
addedTaylor's theorem (informal description)99c0f5e45cda
addedLinear approximation1daa5f5a293c
addedQuadratic approximation461f7d09a4de
addedQuadratic more accurate than linear4b44d4b9e825
addedError of degree-k approximation24e75d18365e
addedAsymptotic nature of Taylor's theorem60ccbe8c12f0
addedTaylor polynomialffcd91ccfa22
addedUniqueness of asymptotic best-fit polynomial9e8e59fd8592
addedRemainder term39121b8c33cb
addedTaylor's theorem (Peano form)b40a88e2dbcd
addedGeneral mean value form of the remainder4fe4c60bc9e3
addedMean-value forms of the remainder7344a520659d
addedIntegral form of the remainder7a4dd8cd9748
addedRemainder estimate from derivative boundsada33f78ee6f
addedUniform estimatee46d487b9d79
addedApproximating the exponential function7917bc8f19c4
addedReal analytic function34fee9d55b7f
addedCauchy–Hadamard formula9ebe4a4a0778
addedUniform convergence of power seriesf87b8828b15b
addedTaylor polynomials of analytic functions7284fa0749c9
addedConvergence of Taylor series6172f135c7be
addedTaylor series (infinite order Taylor polynomial)13e653d45628
addedUniform remainder boundbf6ba1825264
addedUniform convergence to analytic limit905d9b0abb49
addedNon-analytic smooth (flat) functionf49a220b1167
addedComplex generalization of Taylor's theorem1c455caafa1e
addedCauchy's integral formula representation7c3759069704
addedComplex differentiability implies infinite differentiabilitybf2ced1d45b6
addedCauchy's estimate740c6a03e549
addedComplex differentiable implies complex analytic817d239859c2
addedBoundary domination of approximation quality569d5f2a4af0
addedMeromorphic extension and radius of convergenceeeb9936c0260
addedDifferentiability in several variables354129dfc980
addedDifferential of f at a67c4dbf37742
addedMulti-index notation4eb6504316df
addedk times differentiable at a point94a293d702b5
addedMultivariate exact remainder formulad00af69ad030
addedMultivariate uniform estimatesbad7368f42a6
addedMultivariate version of Taylor's theorem5a28465845f7
addedThird-order Taylor polynomial in two dimensions770da67ddf2f