Predefined Functions and Operators

ℯ (Euler’s number)

Alt + e

ί (Imaginary unit)

Alt + i

π

Alt + p or pi

° (Degree symbol)

Alt + o or deg

Addition

+

Subtraction

-

Multiplication

* or Space key

Scalar product

* or Space key

Vector product(see Points and Vectors)

⊗

Division

/

Exponentiation

^ or superscript (x^2 or x2)

Factorial

!

Parentheses

( )

x-coordinate

x( )

y-coordinate

y( )

z-coordinate

z( )

Argument (also works for 3D points / vectors)

arg( )

Conjugate

conjugate( )

Real

real( )

Imaginary

imaginary( )

Absolute value

abs( )

Altitude angle (for 3D points / vectors)

alt( )

Sign

sgn( ) or sign()

Greatest integer less than or equal

floor( )

Least integer greater than or equal

ceil( )

Round to nearest integer (or to y decimal places)

round(x) or round(x, y)

Square root

sqrt( )

Cubic root

cbrt( )

The nth root of x

nroot(x, n)

Random number between 0 and 1

random( )

Exponential function

exp( ) or ℯ^x

Logarithm (natural, to base e)

ln( )

Logarithm to base 2

log₂() or ld( )

Logarithm to base 10

log₁₀( ) or log( ) or lg( )

Logarithm of x to base b

log(b, x )

Cosine

cos( )

Sine

sin( )

Tangent

tan( )

Secant

sec()

Cosecant

csc() or cosec()

Cotangent

cot() or cotan()

Arc cosine (answer in radians)

acos( ) or arccos( )

Arc cosine (answer in degrees)

acosd( )

Arc sine (answer in radians)

asin( ) or arcsin( )

Arc sine (answer in degrees)

asind( )

Arc tangent (answer in radians, between -π/2 and π/2)

atan( ) or arctan( )

Arc tangent (answer in degrees, between -90° and 90°)

atand( )

Arc tangent (answer in radians, between -π and π)

atan2(y, x)

Arc tangent (answer in degrees, between -180° and 180°)

atan2d(y, x)

Hyperbolic cosine

cosh( )

Hyperbolic sine

sinh( )

Hyperbolic tangent

tanh( )

Hyperbolic secant

sech( )

Hyperbolic cosecant

csch( )

Hyperbolic cotangent

coth( ) or cotanh()

Antihyperbolic cosine

acosh( ) or arccosh( )

Antihyperbolic sine

asinh( ) or arcsinh( )

Antihyperbolic tangent

atanh( ) or arctanh( )

Beta function Β(a, b)

beta(a, b)

Incomplete beta function Β(x;a, b)

beta(a, b, x)

Incomplete regularized beta function I(x; a, b)

betaRegularized(a, b, x)

Gamma function Γ(x)

gamma( x)

(Lower) incomplete gamma function γ(a, x)

gamma(a, x)

(Lower) incomplete regularized gamma function P(a

gammaRegularized(a, x)

Gaussian Error Function

erf(x)

Digamma function

psi(x)

The Polygamma function is the (m+1)th derivative of the natural logarithm of the Gamma function, gamma(x) (m=0,1)

polygamma(m, x)

The Sine Integral function

sinIntegral(x)

The Cosine Integral function

cosIntegral(x)

The Exponential Integral function

expIntegral(x)

The Riemann-Zeta function ζ(x)

zeta(x)

Lambert’s W function LambertW(x, branch)

LambertW(x, 0), LambertW(x, -1)