### 41-XX 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 be assigned at least one classification number from 01-XX)
- 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, Nikolskiui type inequalities)
- 41A20 Approximation by rational functions
- 41A21 Pade 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

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