The Pochhammer symbol or rising factorial often appears in series expansions for hypergeometric functions.
The Pochammer symbol has a definite value even when the gamma functions which appear in its definition are infinite.
Pochhammer[a, n]Product of the first 3 numbers:
Pochhammer[1, 3]
Pochhammer[1, n] is the same as Pochhammer[2, n-1] since 1 is a multiplicative identity.
Pochhammer[1, 3] == Pochhammer[2, 2]
Although sometimes Pochhammer[0, n] is taken to be 1, in Mathics it is 0:
Pochhammer[0, n]
Pochhammer uses Gamma for non-Integer values of n:
Pochhammer[1, 3.001]
Pochhammer[1, 3.001] == Pochhammer[2, 2.001]
Pochhammer[1.001, 3] == 1.001 2.001 3.001