Difference between revisions of "Orthogonality of Laguerre L"
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(Created page with "==Theorem== The following formula holds: $$\displaystyle\int_0^{\infty} e^{-x} L_n(x) L_m(x) \mathrm{d}x = \delta_{mn},$$ where $e^{-x}$ denotes the exponential, $L_n$ den...") |
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==References== | ==References== | ||
| − | * {{BookReference|Special Functions for Scientists and Engineers|1968|W.W. Bell|prev=L n'(0)=-n|next= | + | * {{BookReference|Special Functions for Scientists and Engineers|1968|W.W. Bell|prev=L n'(0)=-n|next=(n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x)}}: Theorem 6.4 |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 14:30, 15 March 2018
Theorem
The following formula holds: $$\displaystyle\int_0^{\infty} e^{-x} L_n(x) L_m(x) \mathrm{d}x = \delta_{mn},$$ where $e^{-x}$ denotes the exponential, $L_n$ denotes Laguerre L, and $\delta$ denotes Kronecker delta.
Proof
References
- 1968: W.W. Bell: Special Functions for Scientists and Engineers ... (previous) ... (next): Theorem 6.4
