Difference between revisions of "L n(x)=(e^x/n!)d^n/dx^n(x^n e^(-x))"
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(Created page with "==Theorem== The following formula holds: $$L_n(x) = \dfrac{e^x}{n!} \dfrac{d^n}{dx^n} (x^n e^{-x}),$$ where $L_n$ denotes Laguerre L and $e^x$ denotes the exponential...") |
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==Theorem== | ==Theorem== | ||
The following formula holds: | The following formula holds: | ||
| − | $$L_n(x) = \dfrac{e^x}{n!} \dfrac{d^n}{ | + | $$L_n(x) = \dfrac{e^x}{n!} \dfrac{\mathrm{d}^n}{\mathrm{d}x^n} (x^n e^{-x}),$$ |
where $L_n$ denotes [[Laguerre L]] and $e^x$ denotes the [[exponential]] function. | where $L_n$ denotes [[Laguerre L]] and $e^x$ denotes the [[exponential]] function. | ||
| Line 7: | Line 7: | ||
==References== | ==References== | ||
| − | * {{BookReference|Special Functions for Scientists and Engineers|1968|W.W. Bell|prev=Generating function for Laguerre L|next= | + | * {{BookReference|Special Functions for Scientists and Engineers|1968|W.W. Bell|prev=Generating function for Laguerre L|next=L n(0)=1}}: Theorem 6.2 |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 14:15, 15 March 2018
Theorem
The following formula holds: $$L_n(x) = \dfrac{e^x}{n!} \dfrac{\mathrm{d}^n}{\mathrm{d}x^n} (x^n e^{-x}),$$ where $L_n$ denotes Laguerre L and $e^x$ denotes the exponential function.
Proof
References
- 1968: W.W. Bell: Special Functions for Scientists and Engineers ... (previous) ... (next): Theorem 6.2
