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Approximations and expansions

{For all approximation theory in the complex domain, see 30Exx, 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42Axx, 42A10 and 42A15; for numerical approximation, see 65Dxx}

41-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
41-01 Instructional exposition (textbooks, tutorial papers, etc.)
41-02 Research exposition (monographs, survey articles)
41-03 Historical (must also be assigned at least one classification number from Section 01)
41-04 Explicit machine computation and programs (not the theory of computation or programming)
41-06 Proceedings, conferences, collections, etc.


41A05 Interpolation
[See also 42A15 and 65D05]
41A10 Approximation by polynomials
{For approximation by trigonometric polynomials, see 42A10}
41A15 Spline approximation
41A17 Inequalities in approximation (Bernstein, Jackson, Nikoľskii-type inequalities)
41A20 Approximation by rational functions
41A21 Padé approximation
41A25 Rate of convergence, degree of approximation
41A27 Inverse theorems
41A28 Simultaneous approximation
41A29 Approximation with constraints
41A30 Approximation by other special function classes
41A35 Approximation by operators (in particular, by integral operators)
41A36 Approximation by positive operators
41A40 Saturation
41A44 Best constants
41A45 Approximation by arbitrary linear expressions
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
41A50 Best approximation, Chebyshev systems
41A52 Uniqueness of best approximation
41A55 Approximate quadratures
41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
[See also 30E15]
41A63 Multidimensional problems (should also be assigned at least one other classification number in this section)
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A80 Remainders in approximation formulas
41A99 Miscellaneous topics