Theorem 1 relates the quantity $a(n)$ to the quantity $b(n)$.
A natural question to ask is how the quantities $A(S,T)$ and $B(S,T)$ vary as $S$ and $T$ change.
The quantities $F$ and $G$ differ by an arbitrarily small amount.
Generally we add a tilde to distinguish between quantities associated with $\tilde{G}$ and those associated with $G$.
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