ISO 80000-2

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ISO 80000-2:2009 is a standard describing mathematical signs and symbols developed by the International Organization for Standardization (ISO), superseding ISO 31-11 [1] The Standard, whose full name is Quantities and units — Part 2: Mathematical signs and symbols to be used in the natural sciences and technology, is a part of the group of standards called ISO/IEC 80000.

Contents list

The Standard is divided into the following chapters:

  • Foreword
  • Introduction
  1. Scope
  2. Normative references
  3. Variables, functions, and operators
  4. Mathematical logic
  5. Sets
  6. Standard number sets and intervals
  7. Miscellaneous signs and symbols
  8. Elementary geometry
  9. Operations
  10. Combinatorics
  11. Functions
  12. Exponential and logarithmic functions
  13. Circular and hyperbolic functions
  14. Complex numbers
  15. Matrices
  16. Coordinate systems
  17. Scalars, vectors, and tensors
  18. Transforms
  19. Special functions
  • Annex A (normative) - Clarification of the symbols used
  • Bibliography

Symbols for variables and constants

Clause 3 specifies that variables such as x and y, and functions in general (e.g., ƒ(x)) are printed in italic type, while mathematical constants and functions that do not depend on the context (e.g., sin(x + π)) are in roman (upright) type. Examples given of mathematical (upright) constants are e, π and i. The numbers 1, 2, 3, etc. are also upright.

Function symbols and definitions

Clause 13 defines trigonometric and hyperbolic functions such as sin and tanh and their respective inverses arcsin and artanh.

Clause 19 defines numerous special functions, including the gamma function, Riemann zeta function, beta function, exponential integral, logarithmic integral, sine integral, Fresnel integrals, error function, incomplete elliptic integrals, hypergeometric functions, Legendre polynomials, spherical harmonics, Hermite polynomials, Laguerre polynomials, Chebyshev polynomials, Bessel functions, Neumann functions, Hankel functions and Airy functions.


  1. "ISO 80000-2:2009". International Organization for Standardization. Retrieved 1 July 2010.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>