Method on @sym: pochhammer (x, n) ¶

Rising Factorial or Pochhammer symbol.

Example:

syms x n
pochhammer (x, n)
  ⇒ (sym) RisingFactorial(x, n)

The Pochhammer symbol can be defined in terms of the Gamma function:

syms x positive
rewrite (pochhammer (x, n), 'gamma')
  ⇒ (sym)

      Γ(n + x)
      ────────
        Γ(x)

For positive integer n, the result has a simple form:

pochhammer (x, 4)
  ⇒ (sym) x⋅(x + 1)⋅(x + 2)⋅(x + 3)

See also: @sym/gamma, @double/pochhammer.

Package: symbolic