Difference between revisions of "(n+1)L (n+1)(x) = (2n+1-x)L n(x)-nL (n-1)(x)"
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(Created page with "==Theorem== The following formula holds: $$(n+1)L_{n+1}(x)=(2n+1-x)L_n(x)-nL_{n-1}(x),$$ where $L_{n+1}$ denotes Laguerre L. ==Proof== ==References== * {{BookReference|S...") |
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| − | * {{BookReference|Special Functions for Scientists and Engineers|1968|W.W. Bell|prev=Orthogonality of Laguerre L|next= | + | * {{BookReference|Special Functions for Scientists and Engineers|1968|W.W. Bell|prev=Orthogonality of Laguerre L|next=xL n'(x)=nL n(x)-n L (n-1)(x)}}: Theorem 6.5 (i) |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 14:32, 15 March 2018
Theorem
The following formula holds: $$(n+1)L_{n+1}(x)=(2n+1-x)L_n(x)-nL_{n-1}(x),$$ where $L_{n+1}$ denotes Laguerre L.
Proof
References
- 1968: W.W. Bell: Special Functions for Scientists and Engineers ... (previous) ... (next): Theorem 6.5 (i)
