`pochhammer`

Pochhammer symbol (rising factorial) (x)_n.

Category: Mathematics > Mathematical Functions

Syntax

P = pochhammer(x, n)

Returns x*(x+1)*...*(x+n-1), that is gamma(x+n)/gamma(x).

Description

The Pochhammer symbol multiplies n consecutive terms starting at x and increasing by one. With x = 1 it is factorial(n). It appears in the coefficients of hypergeometric series.

With a symbolic base and a symbolic n the call stays symbolic; with exact symbolic numbers the result is an exact rational.

Input arguments

x: Base value, numeric or symbolic.
n: Number of factors; usually a nonnegative integer.

Output arguments

P: The rising factorial.

Example

Rising factorials

pochhammer(3, 4)
pochhammer(sym(1)/2, 3)
pochhammer(1, 5)

Output

ans = 360
ans = 15/8
ans = 120

pochhammer