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Recently Referred Formulae

Adenin
\purinev{4==NH$\mathrm{_2}$;6==H;2==H;1==H}
The Example Formula
f(x)=\int_0^{x}g(t)\,dt
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&& b_j \oplus b_i^{-1} \\
&& = (a_0 \oplus \cdots \oplus a_j) \oplus (a_0 \oplus \cdots \oplus a_i)^{-1} \\
&& = (a_0 \oplus \cdots \oplus a_j) \oplus (a_i^{-1} \oplus \cdots \oplus a_0^{-1}) \\
&& = (a_0 \oplus a_0^{-1}) \oplus \cdots \oplus (a_i \oplus a_i^{-1}) \oplus (a_{i 1} \oplus \cdots \oplus a_j) \\
&& = a_{i 1} \oplus \cdots \oplus a_j
X_N^{(2)} &=& \frac{X_0}{N}R_1 R_2 \cdots R_N   \frac{X_0}{N} R_2 R_3 \cdots R_N   \cdots   \frac{X_0}{N}R_N \\
          &=& \frac{X_0}{N} (R_1 \cdots R_N   R_2 \cdots R_N   \cdots   R_N) \\
          &=& \frac{X_0}{N} \sum_{i=1}^N \prod_{j=i}^N R_j \\
          &\equiv& \frac{X_0}{N} \sum_{i=1}^N {\cal R}_i