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Fungrim entry: 6419ac

ζ ⁣(2,a)=a23F2 ⁣(1,a,a,a+1,a+1,1)\zeta\!\left(2, a\right) = {a}^{-2} \,{}_3F_2\!\left(1, a, a, a + 1, a + 1, 1\right)
Assumptions:aC{0,1,}a \in \mathbb{C} \setminus \{0, -1, \ldots\}
\zeta\!\left(2, a\right) = {a}^{-2} \,{}_3F_2\!\left(1, a, a, a + 1, a + 1, 1\right)

a \in \mathbb{C} \setminus \{0, -1, \ldots\}
Fungrim symbol Notation Short description
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
    Formula(Equal(HurwitzZeta(2, a), Mul(Pow(a, -2), Hypergeometric3F2(1, a, a, Add(a, 1), Add(a, 1), 1)))),
    Assumptions(Element(a, SetMinus(CC, ZZLessEqual(0)))))

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2021-03-15 19:12:00.328586 UTC