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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

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