## Pochhammer Symbol

A.k.a. Rising Factorial. For an Integer ,

 (1)

where is the Gamma Function and
 (2)

The Notation conflicts with both that for q-Series and that for Gaussian Coefficients, so context usually serves to distinguish the three. Additional identities are
 (3)

 (4)

where is the Digamma Function. The Pochhammer symbol arises in series expansions of Hypergeometric Functions and Generalized Hypergeometric Functions.

Spanier, J. and Oldham, K. B. The Pochhammer Polynomials .'' Ch. 18 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 149-165, 1987.