Skip to main content

Table 2 Values of discrete and continual fluxes

From: Orthogonal and diagonal dimension fluxes of hyperspherical function

Degree of freedom (k) n = 0 H S ( k , n , r ) = n = 0 H S ( k , n , 1 ) 0 + H S ( k , n , 1 ) d n
0 e r 2.71828182846 2.89982256317
1 2er 5.43656365692 5.24809906025
2 2πer 17.0794684453 17.6417407306
3 8πer 68.3178737814 56.964225268
4 12π2(er-1) 203.505142758 139.918441638
5 64π2(er-r-1) 453.706079704 271.32230045
6 60π3[2er-(r+1)2-1] 812.172812098 437.960809928
7 n = 0 768 π 3 r n + 4 Γ ( n + 5 ) 1229.10258235 611.722905550
8 n = 0 1680 π 4 r n + 5 Γ ( n + 6 ) 1628.04409715 759.633692941
9 n = 0 12288 π 4 r n + 6 Γ ( n + 7 ) 1933.28876014 855.051695653
10 n = 0 30240 π 5 r n + 7 Γ ( n + 8 ) 2093.93742907 884.975895298
11 n = 0 245760 π 5 r n + 8 Γ ( n + 9 ) 2095.29352414 851.441651487
12 n = 0 665280 π 6 r n + 9 Γ ( n + 10 ) 1956.27052708 768.011397877
13 n = 0 5898240 π 6 r n + 10 Γ ( n + 11 ) 1717.51550066 653.938458847
50 n = 0 H S ( 50 , n , r ) 0.00000002078 0.00000000526
lim k n = 0 H S ( k , n , r ) = 0 0 lim k 0 H S ( k , n , r ) d n = 0
Σ k 19427.858848843922 -