Maxima Function
pochhammer (n, x)
The Pochhammer symbol. For nonnegative integers n with
n <= pochhammer_max_index
, the expression pochhammer (x, n)
evaluates to the product x (x + 1) (x + 2) ... (x + n - 1)
when n > 0
and
to 1 when n = 0
. For negative n,
pochhammer (x, n)
is defined as (-1)^n / pochhammer (1 - x, -n)
.
Thus
(%i1) pochhammer (x, 3); (%o1) x (x + 1) (x + 2) (%i2) pochhammer (x, -3); 1 (%o2) - ----------------------- (1 - x) (2 - x) (3 - x)
To convert a Pochhammer symbol into a quotient of gamma functions,
(see Abramowitz and Stegun, equation 6.1.22) use makegamma
; for example
When n exceeds pochhammer_max_index
or when n
is symbolic, pochhammer
returns a noun form.
(%i1) pochhammer (x, n); (%o1) (x) n