The Dimensional Fluxes of the Hypercylindrical Function

Table 3

𝑣	𝑎𝑣- polynomial coefficient ∑𝑣𝑎𝑣𝑟^𝑣
0	210+𝜋+12𝜋
1	2𝜋+10+76𝜋
2	1𝜋+5+38𝜋+60𝜋^2
3	1+53𝜋3+38𝜋3+148𝜋^2
4	1+512𝜋+1219𝜋6+37𝜋^2+70𝜋^3
5	1+160𝜋+1219𝜋+3037𝜋^25+582𝜋^35
6	1+1360𝜋+7219𝜋+18037𝜋^2+3097𝜋^35+42𝜋^4
7	1+12520𝜋+50419𝜋+126037𝜋^2+21097𝜋^3+351150𝜋^421
8	1+120160𝜋+403219𝜋+1008037𝜋^2+168097𝜋^3+280575𝜋^4+8433𝜋^55
9	1+1181440𝜋+3628819𝜋+9072037𝜋^2+1512097𝜋^3+2520575𝜋^4+7562279𝜋^5126
10	1+11814400𝜋+36288019𝜋+90720037𝜋^2[phone]𝜋^3[phone]𝜋^4[phone]𝜋^5+1260143𝜋^630
11	1+119958400𝜋+399168019𝜋+997920037𝜋^2[phone]𝜋^3[phone]𝜋^4[phone]𝜋^5[phone]𝜋^6198
12	1+147900160+239500800𝜋19𝜋+11975040037𝜋^2[phone]𝜋^3[phone]𝜋^4[phone]𝜋^5[phone]𝜋^6+237613𝜋^712