Generalized Pochhammer symbol
Encyclopedia
In mathematics
, the generalized Pochhammer symbol of parameter
and partition
generalizes the classical Pochhammer symbol
, named after Leo August Pochhammer
, and is defined as
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the generalized Pochhammer symbol of parameter
and partitionPartition (number theory)
In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered to be the same partition; if order matters then the sum becomes a...
generalizes the classical Pochhammer symbolPochhammer symbol
In mathematics, the Pochhammer symbol introduced by Leo August Pochhammer is the notation ', where is a non-negative integer. Depending on the context the Pochhammer symbol may represent either the rising factorial or the falling factorial as defined below. Care needs to be taken to check which...
, named after Leo August Pochhammer
Leo August Pochhammer
Leo August Pochhammer was a Prussian mathematician, known for his work on special functions...
, and is defined as