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Pochhammer’s Symbol

Pochhammer’s  symbol is defined by

(x) _ n = x(x + 1) ...(x + n - 1)

It is also called raising factorial, and it can be derived from Gamma function   in the form

(x) _ n = Γ(x + n)/Γ(x) .

This shows that where the Gamma function has infinite vales, the Pochhammer symbol has definite values.

The Pochhammer symbol satisfies the multiplicative relation

(x) _ m = m^m Underoverscript[∏, k = 0, arg3] ((z + k)/m) _ 1 .

Pochhammer’s symbol plays an important role in the abbreviation of the notation in series expansion for hypergeometric functions.

Cite this web-page as:

Štefan Porubský: Pochhammer’s Symbol.

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