Fungrim entry: 7cb17f

Table of

\zeta\!\left(2 n\right)

for

1 \le n \le 20

$2 n$	$\zeta\!\left(2 n\right)$
2	$\frac{1}{6} {\pi}^{2}$
4	$\frac{1}{90} {\pi}^{4}$
6	$\frac{1}{945} {\pi}^{6}$
8	$\frac{1}{9450} {\pi}^{8}$
10	$\frac{1}{93555} {\pi}^{10}$
12	$\frac{691}{638512875} {\pi}^{12}$
14	$\frac{2}{18243225} {\pi}^{14}$
16	$\frac{3617}{325641566250} {\pi}^{16}$
18	$\frac{43867}{38979295480125} {\pi}^{18}$
20	$\frac{174611}{1531329465290625} {\pi}^{20}$

$2 n$	$\zeta\!\left(2 n\right)$
22	$\frac{155366}{13447856940643125} {\pi}^{22}$
24	$\frac{236364091}{201919571963756521875} {\pi}^{24}$
26	$\frac{1315862}{11094481976030578125} {\pi}^{26}$
28	$\frac{6785560294}{564653660170076273671875} {\pi}^{28}$
30	$\frac{6892673020804}{5660878804669082674070015625} {\pi}^{30}$
32	$\frac{7709321041217}{62490220571022341207266406250} {\pi}^{32}$
34	$\frac{151628697551}{12130454581433748587292890625} {\pi}^{34}$
36	$\frac{26315271553053477373}{20777977561866588586487628662044921875} {\pi}^{36}$
38	$\frac{308420411983322}{2403467618492375776343276883984375} {\pi}^{38}$
40	$\frac{261082718496449122051}{20080431172289638826798401128390556640625} {\pi}^{40}$

Table data:

\left(n, y\right)

such that

\zeta\!\left(n\right) = y

Definitions:

Fungrim symbol	Notation	Short description
`RiemannZeta`	$\zeta\!\left(s\right)$	Riemann zeta function
`Pow`	${a}^{b}$	Power
`ConstPi`	$\pi$	The constant pi (3.14...)

Source code for this entry:

Entry(ID("7cb17f"),
    Description("Table of", RiemannZeta(Mul(2, n)), "for", LessEqual(1, n, 20)),
    Table(TableRelation(Tuple(n, y), Equal(RiemannZeta(n), y)), TableHeadings(Mul(2, n), RiemannZeta(Mul(2, n))), TableSplit(2), List(Tuple(2, Mul(Div(1, 6), Pow(ConstPi, 2))), Tuple(4, Mul(Div(1, 90), Pow(ConstPi, 4))), Tuple(6, Mul(Div(1, 945), Pow(ConstPi, 6))), Tuple(8, Mul(Div(1, 9450), Pow(ConstPi, 8))), Tuple(10, Mul(Div(1, 93555), Pow(ConstPi, 10))), Tuple(12, Mul(Div(691, 638512875), Pow(ConstPi, 12))), Tuple(14, Mul(Div(2, 18243225), Pow(ConstPi, 14))), Tuple(16, Mul(Div(3617, 325641566250), Pow(ConstPi, 16))), Tuple(18, Mul(Div(43867, 38979295480125), Pow(ConstPi, 18))), Tuple(20, Mul(Div(174611, 1531329465290625), Pow(ConstPi, 20))), Tuple(22, Mul(Div(155366, 13447856940643125), Pow(ConstPi, 22))), Tuple(24, Mul(Div(236364091, 201919571963756521875), Pow(ConstPi, 24))), Tuple(26, Mul(Div(1315862, 11094481976030578125), Pow(ConstPi, 26))), Tuple(28, Mul(Div(6785560294, 564653660170076273671875), Pow(ConstPi, 28))), Tuple(30, Mul(Div(6892673020804, 5660878804669082674070015625), Pow(ConstPi, 30))), Tuple(32, Mul(Div(7709321041217, 62490220571022341207266406250), Pow(ConstPi, 32))), Tuple(34, Mul(Div(151628697551, 12130454581433748587292890625), Pow(ConstPi, 34))), Tuple(36, Mul(Div(26315271553053477373, 20777977561866588586487628662044921875), Pow(ConstPi, 36))), Tuple(38, Mul(Div(308420411983322, 2403467618492375776343276883984375), Pow(ConstPi, 38))), Tuple(40, Mul(Div(261082718496449122051, 20080431172289638826798401128390556640625), Pow(ConstPi, 40))))))

Topics using this entry

Riemann zeta function