Table 1 The first seven values of $\mathit{\zeta }\mathbf{(}\mathbf{2}\mathit{n}\mathbf{)}$ , $\mathit{C}\mathbf{(}\mathit{n}\mathbf{)}$ and $\mathit{D}\mathbf{(}\mathit{n}\mathbf{)}$

ζ(2n)

$\frac{{\pi }^2}{6}$

$\frac{{\pi }^4}{90}$

$\frac{{\pi }^6}{945}$

$\frac{{\pi }^8}{9,450}$

$\frac{{\pi }^{10}}{93,555}$

$\frac{691{\pi }^{12}}{638,512,875}$

$\frac{2{\pi }^{14}}{18,243,225}$

C(n)

$\frac{b-a}{4}$

$\frac{{(b-a)}^3}{48}$

$\frac{{(b-a)}^5}{480}$

$\frac{17{(b-a)}^7}{80,640}$

$\frac{31{(b-a)}^9}{1,451,520}$

$\frac{691{(b-a)}^{11}}{9,123,840}$

$\frac{(2^{14}-1){(b-a)}^{13}}{2^{13}\times 18,243,225}$

D(n)

$\frac{b-a}{4}$

$\frac{{(b-a)}^3}{192}$

$\frac{{(b-a)}^5}{20,480}$

$\frac{{(b-a)}^7}{4,128,768}$

$\frac{{(b-a)}^9}{1,358,954,496}$

$\frac{{(b-a)}^{11}}{664,377,753,600}$

$\frac{{(b-a)}^{13}}{13{(6!)}^2{4}^{13}}$