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### Basic Rules

• 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

### 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]. 