Difference between revisions of "Generating function for Laguerre L"
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(Created page with "==Theorem== The following formula holds: $$\dfrac{e^{\frac{-xt}{1-t}}}{1-t} = \displaystyle\sum_{k=0}^{\infty} L_k(x)t^k,$$ where $e^{\frac{-xt}{1-t}}$ denotes an exponentia...") |
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==References== | ==References== | ||
| − | * {{BookReference|Special Functions for Scientists and Engineers|1968|W.W. Bell|prev=Laguerre L|next=L n(x)=(e^x/n!)d^n/dx^n | + | * {{BookReference|Special Functions for Scientists and Engineers|1968|W.W. Bell|prev=Laguerre L|next=L n(x)=(e^x/n!)d^n/dx^n(x^n e^(-x))}}: Theorem 6.1 |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 14:08, 15 March 2018
Theorem
The following formula holds: $$\dfrac{e^{\frac{-xt}{1-t}}}{1-t} = \displaystyle\sum_{k=0}^{\infty} L_k(x)t^k,$$ where $e^{\frac{-xt}{1-t}}$ denotes an exponential function and $L_k$ denotes Laguerre L.
Proof
References
- 1968: W.W. Bell: Special Functions for Scientists and Engineers ... (previous) ... (next): Theorem 6.1
