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Basic Rules

  • Names of functions start with capital letters.
  • Arguments of functions are put inside square brackets.
  • Multiplication is indicated by a space.

    Example: Type Sqrt[Sin[x]] for the square root of the sine of x.

Note: Links in the first column of the following tables will take you to more information about a particular function in the online Documentation Center. Links in the second column will take you to more information about the function in Eric Weisstein's World of Mathematics.

Elementary Operations and Functions

Basic Arithmetic Operations

a + b plus
a - b minus
a b or a*b times
a/b divide
a^b power
Sqrt[a] square root

Mathematical Constants

Pi 3.14159
Degree Pi /180
I Sqrt[-1]
E e
GoldenRatio (1 + Sqrt[5])/2
EulerGamma Euler's constant
Catalan Catalan's constant
StieltjesGamma[n] Stieltjes constants

Trigonometric and Exponential Functions

Sin[x], Cos[x], Tan[x],
Csc[x], Sec[x], Cot[x]
trigonometric functions
(with arguments in radians)
ArcSin[x], ArcCos[x], ArcTan[x],
ArcCsc[x], ArcSec[x], ArcCot[x]
inverse trigonometric functions
(giving results in radians)
Exp[x] or E^x exponential function
b^x b to the power x
Log[x] logarithm of x to the base e
Log[b, x] logarithm of x to the base b
Sinh[x], Cosh[x], Tanh[x],
Csch[x], Sech[x], Coth[x]
hyperbolic functions
ArcSinh[x], ArcCosh[x], ArcTanh[x],
ArcCsch[x], ArcSech[x], ArcCoth[x]
inverse hyperbolic functions

Higher Mathematical Functions

Mathematica includes over five hundred higher mathematical functions, including almost all of the functions of mathematical physics.

  • Names of functions are usually complete English words.

  • Mathematical functions that are usually referred to by a person's name have names in Mathematica of the form PersonSymbol. For example, the Legendre polynomials are denoted by LegendreP[n, x].

  • If the standard notation for a mathematical function involves both subscripts and superscripts, the subscript is given before the superscript in the Mathematica form. For example, the associated Legendre polynomials are denoted as LegendreP[n, m, x].