Gamma recurrence relation

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Theorem

The following formula holds: $$\Gamma(z+1) = z\Gamma(z),$$ where $\Gamma$ denotes the gamma function.

Proof

References

  • 1920: {{ #if: |{{{2}}}|Edmund Taylor Whittaker}}{{#if: George Neville Watson|{{#if: |, {{ #if: |{{{2}}}|George Neville Watson}}{{#if: |, [[Mathematician:{{{author3}}}|{{ #if: |{{{2}}}|{{{author3}}}}}]]{{#if: |, [[Mathematician:{{{author4}}}|{{ #if: |{{{2}}}|{{{author4}}}}}]]{{#if: |, [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]] and [[Mathematician:{{{author6}}}|{{ #if: |{{{2}}}|{{{author6}}}}}]]| and [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]]}}| and [[Mathematician:{{{author4}}}|{{ #if: |{{{2}}}|{{{author4}}}}}]]}}| and [[Mathematician:{{{author3}}}|{{ #if: |{{{2}}}|{{{author3}}}}}]]}}| and {{ #if: |{{{2}}}|George Neville Watson}}}}|}}: [[Book:Edmund Taylor Whittaker/A course of modern analysis{{#if: |/Volume {{{volume}}}|}}{{#if: Third edition|/Third edition}}|A course of modern analysis{{#if: |: Volume {{{volume}}}|}}{{#if: |: {{{eddisplay}}}|{{#if: | ({{{ed}}} ed.)}}}}]]{{#if: | (translated by [[Mathematician:{{{translated}}}|{{ #if: |{{{2}}}|{{{translated}}}}}]])}}{{#if: |, {{{publisher}}}|}}{{#if: |, ISBN {{{isbn}}}|}}{{#if: Reciprocal gamma written as an infinite product | ... (previous)|}}{{#if: findme | ... (next)|}}{{#if: |: Entry: {{#if: |[[{{{entryref}}}|{{{entry}}}]]|{{{entry}}}}}|}}: $\S 12 \cdot 12$