ISO 80000-2:2009 is a standard describing mathematical signs and symbols developed by the International Organization for Standardization (ISO), superseding ISO 31-11 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.
The Standard is divided into the following chapters:
- Normative references
- Variables, functions, and operators
- Mathematical logic
- Standard number sets and intervals
- Miscellaneous signs and symbols
- Elementary geometry
- Exponential and logarithmic functions
- Circular and hyperbolic functions
- Complex numbers
- Coordinate systems
- Scalars, vectors, and tensors
- Special functions
- Annex A (normative) - Clarification of the symbols used
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.
Additions to ISO 31-11
Examples of additions at an elementary level are the inclusions of int a for the integer part of a real number, frac a for the fractional part of a real number and P (often typset as black board bold) for the set of primes.
Function symbols and definitions
Clause 13 defines trigonometric and hyperbolic functions such as sin and tanh and their respective inverses arcsin and artanh. Note that the popular way of writing these inverses as sin-1 and tanh-1 is not even mentioned in ISO 80000-2.
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.