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Recently Referred Formulae

\frac{iY * (iY 1)}{2} - iY \leq iX \leq \frac{iY * (iY 1)}{2} - 1
\binom{n}{k} = \binom{n-1}{k}   \binom{n-1}{k-1}

\phi(x) = f(x)   \lambda \int_a^x K(x,t)\,\phi(t)\,dt

\phi(x) = f(x)   \lambda \int_a^b K(x,t)\,\phi(t)\,dt
&& 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