gamma - Gamma function

Syntax

Description

gamma(x) returns the gamma function of a symbolic variable or symbolic expression x.

gamma(A) returns the gamma function of the elements of a symbolic vector or a symbolic matrix A.

Input Arguments

x	Symbolic number, variable, or expression.
A	Vector or matrix of symbolic numbers, variables, or expressions.

Definitions

gamma Function

The following integral defines the gamma function:

Examples

Differentiate the gamma function, and then substitute the variable t with the value 1:

syms t
u = diff(gamma(t^3 + 1))
subs(u, 1)

u =
3*t^2*gamma(t^3 + 1)*psi(t^3 + 1)

ans =
    1.2684

Compute the limit of the following expression that involves the gamma function:

syms x
limit(x/gamma(x), x, inf)

ans =
0

Simplify the following expression:

syms x
simplify(gamma(x)*gamma(1 - x))

ans =
pi/sin(pi*x)

See Also

beta | factorial | mfun | mfunlist | nchoosek | psi

How To

• Special Functions of Applied Mathematics

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