Table 2 Values of discrete and continual fluxes

0

e ^r

2.71828182846

2.89982256317

1

2e^r

5.43656365692

5.24809906025

2

2πe^r

17.0794684453

17.6417407306

3

8πe^r

68.3178737814

56.964225268

4

12π²(e^r-1)

203.505142758

139.918441638

5

64π²(e^r-r-1)

453.706079704

271.32230045

6

60π³[2e^r-(r+1)²-1]

812.172812098

437.960809928

7

$\sum _{n=0}^{\infty }\frac{768{\pi }^3{r}^{n+4}}{\Gamma \left(n+5\right)}$

1229.10258235

611.722905550

8

$\sum _{n=0}^{\infty }\frac{1680{\pi }^4{r}^{n+5}}{\Gamma \left(n+6\right)}$

1628.04409715

759.633692941

9

$\sum _{n=0}^{\infty }\frac{12288{\pi }^4{r}^{n+6}}{\Gamma \left(n+7\right)}$

1933.28876014

855.051695653

10

$\sum _{n=0}^{\infty }\frac{30240{\pi }^5{r}^{n+7}}{\Gamma \left(n+8\right)}$

2093.93742907

884.975895298

11

$\sum _{n=0}^{\infty }\frac{245760{\pi }^5{r}^{n+8}}{\Gamma \left(n+9\right)}$

2095.29352414

851.441651487

12

$\sum _{n=0}^{\infty }\frac{665280{\pi }^6{r}^{n+9}}{\Gamma \left(n+10\right)}$

1956.27052708

768.011397877

13

$\sum _{n=0}^{\infty }\frac{5898240{\pi }^6{r}^{n+10}}{\Gamma \left(n+11\right)}$

1717.51550066

653.938458847

$⋮$

$⋮$

$⋮$

$⋮$

50

$\sum _{n=0}^{\infty }HS\left(50,n,r\right)$

0.00000002078

0.00000000526

$⋮$

$⋮$

$⋮$

$⋮$

∞

$\underset{k\to \infty }{\text{lim}}\sum _{n=0}^{\infty }HS\left(k,n,r\right)=0$

0

$\underset{k\to \infty }{\text{lim}}\underset{0}{\overset{\infty }{\int }}HS\left(k,n,r\right)dn=0$

$\underset{k}{\Sigma }$

19427.858848843922

-