Functions

Updated March 28, 2011

a, b, c, x, y, z are used to denote variables and /or expressions below. n is used to denote an integer, V a vector space, and T a linear operator. { and } pairs are always used when appropriate, but they are sometimes optional, for example when a quantity has a subscript or superscript consisting of a single number or letter, as a^2 for a squared or x_i for x subscript i.

Common Functions

 Latex Symbol Meaning \frac{x}{y} fraction with numerator x and denominator y \sqrt{x} square root of x \sqrt[n]{x} n'th root of x \sum_{a}^{b} x Sum from a to b of x \prod_{a}^{b} x Product from a to b of x \int_{a}^{b} x integral from a to b of x

Trig Functions

 Latex Symbol Meaning \cos x cosine of x \sec x secant of x \arccos x arc cosine of x \cosh x hyperbolic cosine of x \sin x sine of x \csc x cosecant of x \arcsin x arc sine of x \sinh x hyperbolic sine of x \tan x tangent of x \cot x cotangent of x \arctan x arc tangent of x \tanh x hyperbolic tangent of x \coth x hyperbolic cotangent of x

Operators

 Latex Symbol Meaning \arg(z) The argument of z; the angle in the polar form of the complex number z \dim V The dimension of V, dimension of the vector space V \exp x exponential of x \hom (G,H) The set of homomorphisms from G to H; the set of morphisms from G to H \ker T The kernel of T; the kernel of the linear operator T \lg x Log of x to base 10 \ln x natural logarithm of x \log x logarithm to base 10 of x \log_n x logarithm to base n of x \varliminf (x_n) The limit of the sequence of infima of (x_n) \varlimsup (x_n) The limit of the sequence of suprema of (x_n) \varinjlim The injective limit (colimit) of a family \varprojlim The projective limit (limit) of a family \det determinant \gcd(n,m) The greatest common divisor of n and m \inf a The infimum of A; the greatest lower bound of A \injlim The injective limit (colimit) of a family \lim_{x\to y} z limit of z as x approaches y \liminf (x_n) The limit of the sequence of infima of (x_n) \limsup (x_n) The limit of the sequence of suprema of (x_n) \max (x,y) maximum of x,y \min (x,y) minimum of x,y \projlim The projective limit (limit) of a family \Pr x The probability of event X \sup a The supremum of A; the least upper bound of A