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Series Multisection

If

\begin{displaymath}
f(x)=f_0+f_1x+f_2x^2+\ldots+f_nx^n+\ldots,
\end{displaymath}

then

\begin{displaymath}
S(n,j)=f_jx^j+f_{j+n}x^{j+n}+f_{j+2n}x^{j+2n}+\ldots
\end{displaymath}

is given by

\begin{displaymath}
S(n,j)={1\over n} \sum_{t=0}^{n-1} w^{-jt} f(w^tx),
\end{displaymath}

where $w=e^{2\pi i/n}$.

See also Series Reversion


References

Honsberger, R. Mathematical Gems III. Washington, DC: Math. Assoc. Amer., pp. 210-214, 1985.




© 1996-9 Eric W. Weisstein
1999-05-26