Rn_floorNorm-class {multIntTestFunc}

An S4 class to represent the function \frac{\Gamma(n/2+1)}{\pi^{n/2}(1+\lfloor \Vert \vec{x} \Vert_2^n \rfloor)^s} on R^n

Description

Implementation of the function

f \colon R^n \to [0,\infty),\, \vec{x} \mapsto f(\vec{x}) = \frac{\Gamma(n/2+1)}{\pi^{n/2}(1+\lfloor \Vert \vec{x} \Vert_2^n \rfloor)^s},

where n \in \{1,2,3,\ldots\} is the dimension of the integration domain R^n = \times_{i=1}^n R and s>1 is a parameter. In this case the integral is know to be

\int_{R^n} f(\vec{x}) d\vec{x} = \zeta(s),

where \zeta(s) is the Riemann zeta function.

Details

The instance needs to be created with two parameters representing n and s.

Slots

dim

An integer that captures the dimension

s

A numeric value bigger than 1 representing a power

Author(s)

Klaus Herrmann

Examples

n <- as.integer(3)
f <- new("Rn_floorNorm",dim=n,s=2)