Pochhammer symbol with non-negative integer subscript

Theorem

The following formula holds: $$(a)_n = \left\{ \begin{array}{ll} 1, & \quad n=0 \\ a(a+1)\ldots(a+n-1), & \quad n=1,2,3,\ldots, \end{array} \right.$$ where $(a)_n$ denotes the Pochhammer symbol.

References

• 1953: {{ #if: |{{{2}}}|Arthur Erdélyi}}{{#if: Wilhelm Magnus|{{#if: Fritz Oberhettinger|, {{ #if: |{{{2}}}|Wilhelm Magnus}}{{#if: Francesco G. Tricomi|, {{ #if: |{{{2}}}|Fritz Oberhettinger}}{{#if: |, {{ #if: |{{{2}}}|Francesco G. Tricomi}}{{#if: |, [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]] and [[Mathematician:{{{author6}}}|{{ #if: |{{{2}}}|{{{author6}}}}}]]| and [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]]}}| and {{ #if: |{{{2}}}|Francesco G. Tricomi}}}}| and {{ #if: |{{{2}}}|Fritz Oberhettinger}}}}| and {{ #if: |{{{2}}}|Wilhelm Magnus}}}}|}}: [[Book:Arthur Erdélyi/Higher Transcendental Functions Volume I{{#if: |/Volume {{{volume}}}|}}{{#if: |/{{{edpage}}}}}|Higher Transcendental Functions Volume I{{#if: |: Volume {{{volume}}}|}}{{#if: |: {{{eddisplay}}}|{{#if: | ({{{ed}}} ed.)}}}}]]{{#if: | (translated by [[Mathematician:{{{translated}}}|{{ #if: |{{{2}}}|{{{translated}}}}}]])}}{{#if: |, {{{publisher}}}|}}{{#if: |, ISBN {{{isbn}}}|}}{{#if: Pochhammer | ... (previous)|}}{{#if: findme | ... (next)|}}{{#if: |: Entry: {{#if: |[[{{{entryref}}}|{{{entry}}}]]|{{{entry}}}}}|}}: $4.1 (2)$