Difference between revisions of "Stirling polynomial"
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(Created page with "The Stirling polynomials $S_k(t)$ are defined by $$S_k(t)=k! \displaystyle\sum_{j=0}^k (-1)^{k-j}\displaystyle\sum_{m=j}^k {{x+m} \choose m}{m \choose j}L_{k+m}^{(-k-j)}(-j),$...") |
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$$S_k(t)=k! \displaystyle\sum_{j=0}^k (-1)^{k-j}\displaystyle\sum_{m=j}^k {{x+m} \choose m}{m \choose j}L_{k+m}^{(-k-j)}(-j),$$ | $$S_k(t)=k! \displaystyle\sum_{j=0}^k (-1)^{k-j}\displaystyle\sum_{m=j}^k {{x+m} \choose m}{m \choose j}L_{k+m}^{(-k-j)}(-j),$$ | ||
where $L_{k+m}^{(-k-j)}$ denotes an [[Associated Laguerre L|associated Laguerre polynomial]]. | where $L_{k+m}^{(-k-j)}$ denotes an [[Associated Laguerre L|associated Laguerre polynomial]]. | ||
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Latest revision as of 18:43, 24 May 2016
The Stirling polynomials $S_k(t)$ are defined by $$S_k(t)=k! \displaystyle\sum_{j=0}^k (-1)^{k-j}\displaystyle\sum_{m=j}^k {{x+m} \choose m}{m \choose j}L_{k+m}^{(-k-j)}(-j),$$ where $L_{k+m}^{(-k-j)}$ denotes an associated Laguerre polynomial.
