Rising Factorial

The rising factorial, denoted x ( n ) superscript 𝑥 𝑛 x^{(n)} or x n ¯ superscript 𝑥 ¯ 𝑛 x^{\overline{n}} , is the Polynomial

x(n)=x⁢(x+1)⁢(x+2)⁢⋯⁢(x+n−1)=∏k=0n−1(x+k)superscript𝑥𝑛𝑥𝑥1𝑥2⋯𝑥𝑛1superscriptsubscriptproduct𝑘0𝑛1𝑥𝑘x^{(n)}=x(x+1)(x+2)\cdots(x+n-1)=\prod_{k=0}^{n-1}(x+k)