[math-fun] I've only now come to understand that 𝜁[s,a] ≠ HurwitzZeta[s,a],

and is instead completely batbleep: \[Zeta](s,a)==\!\(\* UnderoverscriptBox["\[Sum]", RowBox[{"k", "=", "0"}], "\[Infinity]", LimitsPositioning->True] \*SuperscriptBox[\((k + a)\), \(-s\)]\), where any term with k+a==0 is excluded. (Decipher Box Notation by pasting into Mma.) Can someone provide motivation or precedent for this definition? E.g., why not arbitrarily *define* (-n)!, for positive integer n, as Limit[k! + (-1)^n/(k + n)/Gamma@n, k -> -n] ? (See A060746 <http://oeis.org/A060746>.) Or some more useful sequence, say, Bernoulli numbers? —rwg

From the Mma doc: "HurwitzZeta[s,a] gives the Hurwitz zeta function 𝜁(s,a)." Please feel welcome to share my confusion.