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Theory and Modern Applications

Table 1 Values of discrete and continuous fluxes.

From: Orthogonal and diagonal dimension fluxes of hyperspherical function

Degree of freedom (n)

∑ k = 0 ∞ H S ( k , n , 1 ) ≈

∫ 0 ∞ H S ( k , n , 1 ) d k ≈

0

16962.1740457

16962.3520362

1

2117.56926532

2117.48007283

2

291.022289825

291.104223905

3

45.9993260894

45.5712471365

4

8.71952109668

8.20993584833

5

1.87596579993

1.60128605246

6

0.40326040109

0.30739217922

7

0.07910676340

0.05435115208

8

0.01367865325

0.00860415949

9

0.00207449183

0.00121196056

10

0.00027764247

0.00015240808

11

0.00003309744

0.00001722662

12

0.00000354778

0.00000176333

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∞

lim n → ∞ ∑ k = 0 ∞ H S ( k , n , r ) = 0

lim n → ∞ ∫ 0 ∞ H S ( k , n , r ) d k = 0

Σ n

19427.858848843922

-