Orthogonal and diagonal dimension fluxes of hyperspherical function

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 The polinomial coefficients

v	a_v-the polynomial coefficients $\sum_{v} a_{v} r^{v}$
0	3 + 10π
1	3 + 10π + 12π²
2	$\frac{3}{2} + 5 π + 38 π^{2}$
3	$\frac{1}{2} + \frac{5 π}{3} + \frac{38 π^{2}}{3} + 20 π^{3}$
4	$\frac{1}{8} + \frac{5 π}{12} + \frac{19 π^{2}}{6} + 37 π^{3}$
5	$\frac{1}{40} + \frac{π}{12} + \frac{19 π^{2}}{30} + \frac{37 π^{3}}{5} + 14 π^{4}$
6	$\frac{1}{240} + \frac{π}{72} + \frac{19 π^{2}}{180} + \frac{37 π^{3}}{30} + \frac{97 π^{4}}{5}$
7	$\frac{1}{1680} + \frac{π}{504} + \frac{19 π^{2}}{1260} + \frac{37 π^{3}}{210} + \frac{97 π^{4}}{35} + 6 π^{5}$
8	$\frac{1}{13440} + \frac{π}{4032} + \frac{19 π^{2}}{10080} + \frac{37 π^{3}}{1680} + \frac{97 π^{4}}{280} + \frac{575 π^{5}}{84}$
9	$\frac{1}{120960} + \frac{π}{36288} + \frac{19 π^{2}}{90720} + \frac{37 π^{3}}{15120} + \frac{97 π^{4}}{2520} + \frac{575 π^{5}}{756} + \frac{11 π^{6}}{6}$
10	$\frac{1}{1209600} + \frac{π}{362880} + \frac{19 π^{2}}{907200} + \frac{37 π^{3}}{151200} + \frac{97 π^{4}}{25200} + \frac{115 π^{5}}{1512} + \frac{2279 π^{6}}{1260}$
11	$\frac{1}{13305600} + \frac{π}{3991680} + \frac{19 π^{2}}{9979200} + \frac{37 π^{3}}{1663200} + \frac{97 π^{4}}{277200} + \frac{115 π^{5}}{16632} + \frac{2279 π^{6}}{13860} + \frac{13 π^{7}}{30}$
12	$\frac{1}{159667200} + \frac{π}{47900160} + \frac{19 π^{2}}{119750400} + \frac{37 π^{3}}{19958400} + \frac{97 π^{4}}{3326400} + \frac{115 π^{5}}{199584} + \frac{2279 π^{6}}{166320} + \frac{905 π^{7}}{2376}$