Fungrim home page

Fungrim entry: e50a56

Table of ζ ⁣(n)\zeta\!\left(-n\right) for 0n300 \le n \le 30
n-n ζ ⁣(n)\zeta\!\left(-n\right)
0-1/2
-1-1/12
-20
-31/120
-40
-5-1/252
-60
-71/240
-80
-9-1/132
n-n ζ ⁣(n)\zeta\!\left(-n\right)
-100
-11691/32760
-120
-13-1/12
-140
-153617/8160
-160
-17-43867/14364
-180
-19174611/6600
n-n ζ ⁣(n)\zeta\!\left(-n\right)
-200
-21-77683/276
-220
-23236364091/65520
-240
-25-657931/12
-260
-273392780147/3480
-280
-29-1723168255201/85932
-300
Table data: (n,y)\left(n, y\right) such that ζ ⁣(n)=y\zeta\!\left(n\right) = y
Definitions:
Fungrim symbol Notation Short description
RiemannZetaζ ⁣(s)\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

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-17 11:32:46.829430 UTC