41-XX 
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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 }
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41-00
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General reference works (handbooks, dictionaries, bibliographies, etc.)
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41-01
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Instructional exposition (textbooks, tutorial papers, etc.)
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41-02
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Research exposition (monographs, survey articles)
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41-03
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Historical {!must also be assigned at least one classification number from section 01}
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41-04
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Explicit machine computation and programs (not the theory of computation or programming)
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41-06
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Proceedings, conferences, collections, etc.
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41A05
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Interpolation
[See also
42A15
and
65D05 ]
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41A10
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Approximation by polynomials
{For approximation by trigonometric polynomials, see
42A10 }
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41A15
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Spline approximation
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41A17
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Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski\u\i-type inequalities)
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41A20
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Approximation by rational functions
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41A21
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Pad\'e approximation
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41A25
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Rate of convergence, degree of approximation
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41A27
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Inverse theorems
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41A28
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Simultaneous approximation
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41A29
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Approximation with constraints
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41A30
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Approximation by other special function classes
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41A35
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Approximation by operators (in particular, by integral operators)
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41A36
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Approximation by positive operators
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41A40
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Saturation
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41A44
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Best constants
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41A45
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Approximation by arbitrary linear expressions
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41A46
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Approximation by arbitrary nonlinear expressions; widths and entropy
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41A50
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Best approximation, Chebyshev systems
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41A52
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Uniqueness of best approximation
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41A55
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Approximate quadratures
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41A58
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Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
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41A60
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Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
[See also
30E15 ]
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41A63
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Multidimensional problems {!should also be assigned at least one other classification number in this section}
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41A65
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Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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41A80
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Remainders in approximation formulas
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41A99
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Miscellaneous topics
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