D.Bailey, J. Borwein, and D.Bradley found the beautiful pair involving *binomial sums*. In *Theorem 1* of this paper (2008), let *x* *non-zero integer*, then,

When *x* = 0, they reduce into,

However, there is a *third* single-term equality,

*so there might be a third identity* that reduces to this as the special case *x* = 0.

To compare, there are three identities such that as , then those zeta values are the respective limit. For *x* *integer*, then,

The first two were found by Leshchiner and Koecher, respectively, while the third is *Theorem 2* in the same paper by Bailey, Borwein, and Bradley. The function is given in Mathematica as,

while is the *Euler-Mascheroni constant*. So are the Bailey-Borwein-Bradley pair of binomial sum identities in fact *a triplet*?

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