The Hyperspherical Functions of a Derivative

Table 2

Dimension 𝑘	Dimension 𝑛^∗	maxHS	Error 𝜀
0	3.461632144968362	1.129173885450133	1.08⋅10^−16
1	2.461632144968362	2.258347770900258	1.086⋅10^−15
2	1.461632144968362	7.094808766311162	~0
3	0.461632144968362	28.37923506524463	2.665⋅10^−15
4	0	12𝜋^2	0
5	0	32𝜋^2	0
⋮	⋮	⋮	⋮
10	0	6𝜋^5≈1836.18109	0
11	0	128𝜋21^5≈1865.26284	0
12	0	116𝜋^6≈1762.54685	0
⋮	⋮	⋮	⋮
∞	0	lim𝑘→∞HS(𝑘,0,1)=0	0