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Benedict Irwin added section_Inverse_Transform_One_consideration__.tex
over 8 years ago
Commit id: 5c68b4642b718d8df2161cd4ca5e582d9d0442f9
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\section{Inverse Transform}
One consideration is whether there is a one-to-one mapping, and a well defined inverse transform.
Then we could consider if a recursive sum exists that has a Laurent series \begin{equation}
p(x) = \frac{2}{x} - \frac{3}{x^3} + \frac{5}{x^5} - \frac{7}{x^7} + \frac{11}{x^9} - \cdots\\
p(x) = \sum_{k=1}^\infty (-1)^{k+1}\frac{p_k}{x^{(2k-1)}}
\end{equation}
