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Mathematics Subject Classification – MSC2010

Sequences, series, summability 13697

General reference works (handbooks, dictionaries, bibliographies, etc.) 23

Instructional exposition (textbooks, tutorial papers, etc.) 214

Research exposition (monographs, survey articles) 75

Historical (must also be assigned at least one classification number from Section 01) 149

Explicit machine computation and programs (not the theory of computation or programming) 21

Proceedings, conferences, collections, etc. 35

Convergence and divergence of infinite limiting processes 6674

Convergence and divergence of series and sequences 3344

Convergence and divergence of integrals 231

Convergence and divergence of continued fractions [See also 30B70] 971

Convergence and divergence of infinite products 153

Approximation to limiting values (summation of series, etc.) [For the Euler-Maclaurin summation formula, see 65B15] 730

Convergence and divergence of series and sequences of functions 716

Ideal and statistical convergence [See also 40G15] 691

None of the above, but in this section 247

Multiple sequences and series 684

Multiple sequences and series (should also be assigned at least one other classification number in this section) 679

None of the above, but in this section 3

General summability methods 2262

Matrix methods 1875

Integral methods 145

Function-theoretic methods (including power series methods and semicontinuous methods) 145

None of the above, but in this section 118

Direct theorems on summability 1351

General theorems 203

Structure of summability fields 66

Tauberian constants and oscillation limits 26

Convergence factors and summability factors 509

Summability and bounded fields of methods 97

Inclusion and equivalence theorems 493

None of the above, but in this section 36

Inversion theorems 1063

Tauberian theorems, general 993

Growth estimates 28

Lacunary inversion theorems 27

Tauberian constants 10

None of the above, but in this section 25

Absolute and strong summability (should also be assigned at least one other classification number in Section 40) 1145

Absolute and strong summability (should also be assigned at least one other classification number in Section 40) 1141

None of the above, but in this section 3

Special methods of summability 3384

Cesàro, Euler, Nörlund and Hausdorff methods 2051

Abel, Borel and power series methods 621

Summability methods using statistical convergence [See also 40A35] 158

None of the above, but in this section 802

Functional analytic methods in summability 612

Functional analytic methods in summability 609

None of the above, but in this section 3

Summability in abstract structures [See also 43A55, 46A35, 46B15] 549

Summability in abstract structures [See also 43A55, 46A35, 46B15] (should also be assigned at least one other classification number in this section) 543

None of the above, but in this section 5

Overview

00

General mathematics

01

History and biography

03

Mathematical logic and foundations

05

Combinatorics

06

Order, lattices, ordered algebraic structures

08

General algebraic systems

11

Number theory

12

Field theory and polynomials

13

Commutative algebra

14

Algebraic geometry

15

Linear and multilinear algebra; matrix theory

16

Associative rings and algebras

17

Nonassociative rings and algebras

18

Category theory, homological algebra

19

\(K\)-theory

20

Group theory and generalizations

22

Topological groups, Lie groups

26

Real functions

28

Measure and integration

30

Functions of a complex variable

31

Potential theory

32

Several complex variables and analytic spaces

33

Special functions

34

Ordinary differential equations

35

Partial differential equations

37

Dynamical systems and ergodic theory

39

Difference and functional equations

40

Sequences, series, summability

41

Approximation and expansions

42

Harmonic analysis on Euclidean spaces

43

Abstract harmonic analysis

44

Integral transforms, operational calculus

45

Integral equations

46

Functional analysis

47

Operator theory

49

Calculus of variations and optimal control; optimization

51

Geometry

52

Convex and discrete geometry

53

Differential geometry

54

General topology

55

Algebraic topology

57

Manifolds and cell complexes

58

Global analysis, analysis on manifolds

60

Probability theory and stochastic processes

62

Statistics

65

Numerical analysis

68

Computer science

70

Mechanics of particles and systems

74

Mechanics of deformable solids

76

Fluid mechanics

78

Optics, electromagnetic theory

80

Classical thermodynamics, heat transfer

81

Quantum Theory

82

Statistical mechanics, structure of matter

83

Relativity and gravitational theory

85

Astronomy and astrophysics

86

Geophysics

90

Operations research, mathematical programming

91

Game theory, economics, social and behavioral sciences

92

Biology and other natural sciences

93

Systems theory; control

94

Information and communication, circuits

97

Mathematics education

W3C

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