Fungrim entry: e50a56

Table of

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

for

0 \le n \le 30

$-n$	$\zeta\!\left(-n\right)$
0	-1/2
-1	-1/12
-2	0
-3	1/120
-4	0
-5	-1/252
-6	0
-7	1/240
-8	0
-9	-1/132

$-n$	$\zeta\!\left(-n\right)$
-10	0
-11	691/32760
-12	0
-13	-1/12
-14	0
-15	3617/8160
-16	0
-17	-43867/14364
-18	0
-19	174611/6600

$-n$	$\zeta\!\left(-n\right)$
-20	0
-21	-77683/276
-22	0
-23	236364091/65520
-24	0
-25	-657931/12
-26	0
-27	3392780147/3480
-28	0
-29	-1723168255201/85932
-30	0

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

Source code for this entry:

Entry(ID("e50a56"),
    Description("Table of", RiemannZeta(Neg(n)), "for", LessEqual(0, n, 30)),
    Table(TableRelation(Tuple(n, y), Equal(RiemannZeta(n), y)), TableHeadings(Neg(n), RiemannZeta(Neg(n))), TableSplit(3), List(Tuple(0, Neg(Div(1, 2))), Tuple(-1, Neg(Div(1, 12))), Tuple(-2, 0), Tuple(-3, Div(1, 120)), Tuple(-4, 0), Tuple(-5, Neg(Div(1, 252))), Tuple(-6, 0), Tuple(-7, Div(1, 240)), Tuple(-8, 0), Tuple(-9, Neg(Div(1, 132))), Tuple(-10, 0), Tuple(-11, Div(691, 32760)), Tuple(-12, 0), Tuple(-13, Neg(Div(1, 12))), Tuple(-14, 0), Tuple(-15, Div(3617, 8160)), Tuple(-16, 0), Tuple(-17, Neg(Div(43867, 14364))), Tuple(-18, 0), Tuple(-19, Div(174611, 6600)), Tuple(-20, 0), Tuple(-21, Neg(Div(77683, 276))), Tuple(-22, 0), Tuple(-23, Div(236364091, 65520)), Tuple(-24, 0), Tuple(-25, Neg(Div(657931, 12))), Tuple(-26, 0), Tuple(-27, Div(3392780147, 3480)), Tuple(-28, 0), Tuple(-29, Neg(Div(1723168255201, 85932))), Tuple(-30, 0))))

Topics using this entry

Riemann zeta function