271.23.15  Introduction to analysis, and some special problems in analysis
271.23.15.19  Theory of real numbers
271.23.15.25  Asymptotic formulas and expressions
271.23.15.27  Analytic means.  Inequalities
271.23.15.27.17  Means
271.23.15.27.25  Numerical inequalities and some elementary functional inequalities
271.23.15.33  Study of individual functions
271.23.17  Differential and integral calculus
271.23.17.17  Differential calculus
271.23.17.17.31  Mappings.  Implicit functions
271.23.17.17.33   Other analytic applications of differential calculus
271.23.17.19  Integral calculus
271.23.17.19.31  Red?  integrals
271.23.17.19.31.19  Integrals over curved manifolds (curvilinear and surface integrals)
271.23.17.19.33  Definite simple or multiple integrals
271.23.17.19.33.17  Improper integrals
271.23.19  Functional equations and the theory of finite differences
271.23.19.15.  Theory of finite differences
271.23.19.15.17  Finite-difference equations
271.23.19.15.17.21  Recurrent relations and series
271.23.19.19  Functional equations and inequalities
271.23.21  Integral transformations, operational calculus
271.23.21.17  Laplace transform
271.23.21.19  Fourier integral and Fourier transform
271.23.21.21  Other integral transformations and their inversions.  Convolutions
271.23.21.25  Operational calculus
271.23.23  Series and sequences
271.23.23.15  Numerical and functional series and sequences
271.23.23.15.15  Special numerical series and sequences
271.23.23.15.15.25  Sums of finite and infinite series
271.23.23.15.17  Convergence
271.23.23.15.25  Multiple series and sequences
271.23.23.15.31  Summation theory
271.23.23.15.31.25  Tauberian theorems
271.23.23.19  Infinite products
271.23.23.21  Continued fractions
271.23.25  Special functions
271.23.25.15  Euler integrals and their generalizations.  The gamma function and related 
		functions
271.23.25.17  Probability integral and related functions
271.23.25.19  Elliptic functions and integrals
271.23.25.21  Bessel functions and polynomials and other cylindrical functions
271.23.25.25  Mathieu functions
271.23.25.27  Spherical functions.  Legendre polynomials and functions,  harmonic 
		polynomials, ultraspherical polynomials.  Gegenbauer functions
271.23.25.31  Orthogonal polynomials and their generalizations (Chebyshev, Hermite, 
		Jacobi, Laguerre, et al.)
271.23.25.33  Hypergeometric series and functions.  Generalized and degenerate 	
		hypergeometric  functions and their generalizations
271.23.25.39  Other special functions and special numbers

271.25  Theory of functions of a real variable

271.25.15  Descriptive function theory 
271.25.17  Metric theory of functions
271.25.17.15  Measures, integration and differentiation
271.25.17.15.15  Measure, capacity
271.25.17.15.15.17  Lebesgue measure
271.25.17.15.15.19  Borel measure
271.25.17.15.15.21  Other measures
271.25.17.15.15.23  Measurable functions
271.25.17.15.15.25  Continuous functions
271.25.17.15.15.27  Additive set functions
271.25.17.15.15.29  Capacity
271.25.17.15.17  Integration theory
271.25.17.15.17.15  Riemann integral
271.25.17.15.17.17  Lebesgue integral
271.25.17.15.17.21  Stieltjes integral
271.25.17.15.17.25  Other integrals (theory)
271.25.17.15.19  Singular integrals
271.25.17.15.21  Integrals of potential type
271.25.17.15.23  Differentiation theory
271.25.17.23.17  Differentiable functions
271.25.17.15.23.19  Derivative
271.25.17.15.23.23  Symmetric derivatives
271.25.17.15.27  Mappings
271.25.17.15.29  Curved surfaces
271.25.17.15.29.17  Level sets of functions of several variables
271.25.17.17  Classes (sets) of functions
271.25.17.17.17  Compact families of function
271.25.17.17.17.17  Epsilon nets.  Epsilon entropy
271.25.17.17.17.21  Widths
271.25.17.17.19  Embedding theorems for classes of differentiable functions
271.25.17.17.19.18  Inequalities between partial derivatives
271.25.17.17.19.21  Boundary properties of functions
271.25.17.17.19.25  Weight classes
271.25.17.17.19.31  Extension theorems
271.25.17.17.19.33  Integration of classes of functions
271.25.17.17.21 Functions of bounded variation
271.25.17.17.21.17  Absolutely continuous functions
271.25.17.17.21.21  Convex functions and their generalizations
271.25.17.17.25  Quasi-analytic functions
271.25.17.17.27  Other classes of functions
271.25.17.17.31  Superpositions
271.25.17.17.33  Inequalities
271.25.17.19  Systems of functions and series in systems of functions
271.25.17.19.17  Completeness and closure of system of functions
271.25.17.19.21  Bases
271.25.17.19.27  Orthogonal systems
271.25.17.19.27.17  Convergence of orthogonal series
271.25.17.19.27.27  Summation of orthogonal series
271.25.17.21  Trigonometric series
271.25.17.21.17  Representation of a function in the form of a trigonometric series
271.25.17.21.19  Uniqueness problems
271.25.17.21.25  Fourier series
271.25.17.21.25.17  Convergence of Fourier series
271.25.17.21.25.19 Absolute convergence of Fourier series
271.25.17.21.25.21  Fourier coefficients
271.25.17.21.25.27  Summation of Fourier coefficients
271.25.17.21.31  Multiple trigonometric series
271.25.17.21.31.25  Multiple Fourier series
271.25.17.21.31.27  Summation of multiple Fourier series
271.25.17.25  Theory of the Fourier integral
271.25.17.25.27  Summability of Fourier integrals
271.25.17.27  Almost periodic functions
271.25.17.27.25  Compactness of systems of almost periodic functions
271.25.17.27.27  Convergence and summability of Fourier series of almost periodic 
		functions
271.25.17.27.31  Interpolation, almost periodic extension of functions
271.25.17.27.33  Approximation of almost periodic functions
271.25.19.  Approximation theory 
271.25.19.17  Approximation by algebraic polynomials
271.25.19.17.17  On an infinite domain
271.25.19.17.19  Of several variables
271.25.19.17.27  Chebyshev-type problems
271.25.19.17.33  Approximation with exact constants
271.25.19.19  Approximation by trigonometric polynomials and entire functions of 
		exponential type
271.25.19.19.17  Approximation in the sense of order
271.25.19.19.21  Approximation with exact constants
271.25.19.19.31  Approximation of functions of several variables
271.25.19.21  Approximation by rational functions
271.25.19.21.19  Nonlinear problems in approximation theory
271.25.19.21.25  Approximation in the Hausdorff metric
271.25.19.25  Integration
271.25.19.25.25  Approximation by spline functions
271.25.19.27  Extremal properties of polynomials and their generalizations
271.25.19.27.17  Inequalities for derivatives of polynomials and their generalizations
271.25.19.27.19  Other inequalities for polynomials and their generalizations
271.25.19.27.25  Zeros of polynomials and their generalizations
271.25.19.31  Theory of quadratures and cubatures
271.25.19.33  Moment theory