L n(0)=1
From specialfunctionswiki
Theorem
The following formula holds: $$L_n(0)=1,$$ where $L_n$ denotes Laguerre L.
Proof
References
- 1968: {{ #if: |{{{2}}}|W.W. Bell}}{{#if: |{{#if: |, [[Mathematician:{{{author2}}}|{{ #if: |{{{2}}}|{{{author2}}}}}]]{{#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 [[Mathematician:{{{author2}}}|{{ #if: |{{{2}}}|{{{author2}}}}}]]}}|}}: [[Book:W.W. Bell/Special Functions for Scientists and Engineers{{#if: |/Volume {{{volume}}}|}}{{#if: |/{{{edpage}}}}}|Special Functions for Scientists and Engineers{{#if: |: Volume {{{volume}}}|}}{{#if: |: {{{eddisplay}}}|{{#if: | ({{{ed}}} ed.)}}}}]]{{#if: | (translated by [[Mathematician:{{{translated}}}|{{ #if: |{{{2}}}|{{{translated}}}}}]])}}{{#if: |, {{{publisher}}}|}}{{#if: |, ISBN {{{isbn}}}|}}{{#if: L n(x)=(e^x/n!)d^n/dx^n(x^n e^(-x)) | ... (previous)|}}{{#if: L n'(0)=-n | ... (next)|}}{{#if: |: Entry: {{#if: |[[{{{entryref}}}|{{{entry}}}]]|{{{entry}}}}}|}}: Theorem 6.3 (i)
