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X2X translation formula

Shifting the centre of the exponential expansion from O to $\mbox{\boldmath$\space x $ }_0$we obtain

\begin{eqnarray*}\lefteqn{\sum_{p=1}^{s(\varepsilon)}\sum_{q=1}^{M(p)}
\left(X^...
...\boldmath$ x $ }_0\mbox{\boldmath$ x $ }})_2 \sin \alpha_q(p))},
\end{eqnarray*}


where $X^1_j(p,q;\mbox{\boldmath$\space x $ }_0)$ and $X^2(p,q;\mbox{\boldmath$\space x $ }_0)$ are the coefficients of the exponential expansion at $\mbox{\boldmath$\space x $ }_0$ defined as

\begin{eqnarray*}X^1_j(p,q;\mbox{\boldmath$ x $ }_0)&=&X^1_j(p,q;O)
e^{\script...
...verrightarrow{O\mbox{\boldmath$ x $ }_0})_2 \sin \alpha_q(p))}.
\end{eqnarray*}




Ken-ichi Yoshida
2001-07-28