Skip to main content

Theory and Modern Applications

# Table 3 The polinomial coefficients

v

a v -the polynomial coefficients $\sum _{v}{a}_{v}\phantom{\rule{0.3em}{0ex}}{r}^{v}$

0

3 + 10π

1

3 + 10π + 12π2

2

$\frac{3}{2}+5\pi +38{\pi }^{2}$

3

$\frac{1}{2}+\frac{5\pi }{3}+\frac{38{\pi }^{2}}{3}+20{\pi }^{3}$

4

$\frac{1}{8}+\frac{5\pi }{12}+\frac{19{\pi }^{2}}{6}+37{\pi }^{3}$

5

$\frac{1}{40}+\frac{\pi }{12}+\frac{19{\pi }^{2}}{30}+\frac{37{\pi }^{3}}{5}+14{\pi }^{4}$

6

$\frac{1}{240}+\frac{\pi }{72}+\frac{19{\pi }^{2}}{180}+\frac{37{\pi }^{3}}{30}+\frac{97{\pi }^{4}}{5}$

7

$\frac{1}{1680}+\frac{\pi }{504}+\frac{19{\pi }^{2}}{1260}+\frac{37{\pi }^{3}}{210}+\frac{97{\pi }^{4}}{35}+6{\pi }^{5}$

8

$\frac{1}{13440}+\frac{\pi }{4032}+\frac{19{\pi }^{2}}{10080}+\frac{37{\pi }^{3}}{1680}+\frac{97{\pi }^{4}}{280}+\frac{575{\pi }^{5}}{84}$

9

$\frac{1}{120960}+\frac{\pi }{36288}+\frac{19{\pi }^{2}}{90720}+\frac{37{\pi }^{3}}{15120}+\frac{97{\pi }^{4}}{2520}+\frac{575{\pi }^{5}}{756}+\frac{11{\pi }^{6}}{6}$

10

$\frac{1}{1209600}+\frac{\pi }{362880}+\frac{19{\pi }^{2}}{907200}+\frac{37{\pi }^{3}}{151200}+\frac{97{\pi }^{4}}{25200}+\frac{115{\pi }^{5}}{1512}+\frac{2279{\pi }^{6}}{1260}$

11

$\frac{1}{\text{13305600}}+\frac{\pi }{\text{3991680}}+\frac{19{\pi }^{2}}{\text{9979200}}+\frac{\text{37}{\pi }^{\text{3}}}{\text{1663200}}+\frac{\text{97}{\pi }^{\text{4}}}{\text{277200}}+\frac{\text{1}15{\pi }^{5}}{\text{16632}}+\frac{2279{\pi }^{6}}{13860}+\frac{13{\pi }^{7}}{30}$

12

$\frac{1}{\text{159667200}}+\frac{\pi }{\text{47900160}}+\frac{19{\pi }^{2}}{\text{119750400}}+\frac{\text{37}{\pi }^{\text{3}}}{\text{19958400}}+\frac{\text{97}{\pi }^{\text{4}}}{\text{3326400}}+\frac{\text{1}15{\pi }^{5}}{\text{199584}}+\frac{2279{\pi }^{6}}{166320}+\frac{905{\pi }^{7}}{2376}$