Grim reference (alpha)

RiemannZeta

Input: RiemannZeta(s)
$$\zeta\!\left(s\right)$$

Riemann zeta function.

Input: RiemannZeta(s, 1)
$$\zeta'(s)$$

Differentiated Riemann zeta function.

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

Riemann zeta function differentiated to order $r$.

Symbolic evaluation examples

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

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

Numerical evaluation examples

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

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