Returns an approximation for the numerical integral of the given expression over the given range.

The `integrate`

function returns an approximation for the numerical integral of * f* with the variable

`var`

`a`

`b`

This integral is the same as the area between the function * f* and the x-axis from

`a`

`b`

`f`

`var`

`a`

`b`

`-INF`

or `INF`

to indicate negative or positive infinity.
`integrate`

does not calculate the integral exactly.
Instead the calculation is done using the Gauss-Kronrod 21-point integration rule adaptively to an estimated relative error less than 10f(x)=integrate(t^2-7t+1, t, -3, 15) will integrate f(t)=t^2-7t+1 from -3 to 15 and evaluate to 396. More useful is f(x)=integrate(s*sin(s), s, 0, x). This will plot the definite integral of f(s)=s*sin(s) from 0 to x, which is the same as the indefinite integral of f(x)=x*sin(x).

Returns the summation of an expression evaluated over a range of integers.

The `sum`

function returns the summation of * f* where

`var`

`a`

`b`

* f* may be any function with the variable indicated as the second argument

`var`

`a`

`b`

Returns the product of an expression evaluated over a range of integers.

The `product`

function returns the product of * f* where

`var`

`a`

`b`

* f* may be any function with the variable indicated as the second argument

`var`

`a`

`b`

Returns the factorial of the argument.

The `fact`

function returns the factorial of * n*, commonly written as n!.

`n`

`gamma`

function as fact(n)=gamma(n+1).
Returns the value of the Euler gamma function of the argument.

The `gamma`

function returns the result of the Euler gamma function of * z*, commonly written as Γ(z).

`z`

This cannot be calculated precisely, so Graph is using the Lanczos approximation to calculate the `gamma`

function.

Returns the value of the Euler beta function evaluated for the arguments.

The `beta`

function returns the result of the Euler beta function evaluated for * m* and

`n`

`m`

`n`

`beta`

function relates to the `gamma`

function as
beta(m, n) = gamma(m) * gamma(n) / gamma(m+n).
Returns the value of the Lambert W-function evaluated for the argument.

The `W`

function returns the result of the Lambert W-function, also known as the omega function, evaluated for * z*.

`z`

`W`

function is given by f(W)=W*e
For real values of * z* when

`z`

`W`

function will evaluate to values with an imaginary part.
Returns the value of the Riemann Zeta function evaluated for the argument.

The `zeta`

function returns the result of the Riemann Zeta function, commonly written as ζ(s).
* z* may be any

Returns the remainder of the first argument divided by the second argument.

Calculates * m* modulo

`n`

`mod`

calculates the remainder f, where m = a*n + f for some integer a.
The sign of f is always the same as the sign of `n`

`n`

`mod`

returns 0.
`m`

`n`

Returns the normal distribution of the first argument with optional mean value and standard deviation.

The `dnorm`

function is the probability density of the normal distribution, also called Gaussian distribution.
* x* is the variate, also known as the random variable,

`μ`

`μ`

`μ`

`x`

`μ`