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\begin{eqnarray*} \sum _{x~ =~ s_0}^{x~ =~ u} ~ C_ x ~ \phi _1^{~ x} ~ / ~ \sum _{x~ =~ l}^{x~ =~ u} ~ C_ x ~ \phi _1^{~ x} & = & \alpha / 2 \\[0.10in] \sum _{x~ =~ l}^{x~ =~ s_0} ~ C_ x ~ \phi _2^{~ x} ~ / ~ \sum _{x~ =~ l}^{x~ =~ u} ~ C_ x ~ \phi _2^{~ x} & = & \alpha / 2 \end{eqnarray*}