Grim reference (alpha)

RiemannZeta

Input: RiemannZeta(s)
ζ ⁣(s)\zeta\!\left(s\right)

Riemann zeta function.

Input: RiemannZeta(s, 1)
ζ′(s)\zeta'(s)

Differentiated Riemann zeta function.

Input: RiemannZeta(s, r)
ζ(r)(s){\zeta}^{(r)}(s)

Riemann zeta function differentiated to order rr.

Symbolic evaluation examples

Input: RiemannZeta(4)
ζ ⁣(4)\zeta\!\left(4\right)
Output: Div(Pow(Pi, 4), 90)   (evaluated by pygrim in 0.0011 s)
π490\frac{{\pi}^{4}}{90}

Input: RiemannZeta(0, 1)
ζ′(0)\zeta'(0)
Output: Neg(Div(Log(Mul(2, Pi)), 2))   (evaluated by pygrim in 0.0001 s)
−log⁡ ⁣(2π)2-\frac{\log\!\left(2 \pi\right)}{2}

Numerical evaluation examples

Input: RiemannZeta(3)
ζ ⁣(3)\zeta\!\left(3\right)
Output: RealBall(Decimal("1.2020569031595942854"), Decimal("2.64e-22"))   (evaluated by pygrim in 0.0001 s)
[1.2020569031595942854±2.64⋅10−22]\left[1.2020569031595942854 \pm 2.64 \cdot 10^{-22}\right]

Last updated: 2020-03-06 00:22:16