Unique function in three variables

Algebra Level 4

For \(n > 3, a,b \in \mathbb{R} \), let \(S(n,a,b)\) be defined as

\[\large \displaystyle S(n,a,b) = \sum_{r=0}^{n} (-1)^r \dfrac{(n) \times (n-1) \times . . . . . . .\times (n - r + 1)}{r!} (a-r) (b-r) \]

Find \(\large S(5,\frac{1}{2},\frac{1}{7}) \)

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