The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A339530

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A339530

Decimal expansion of Sum_{k>=1} (zeta(8*k)-1).
(history; published version)

#9 by Vaclav Kotesovec at Fri Jan 22 07:37:56 EST 2021

STATUS

reviewed

approved

#8 by Joerg Arndt at Fri Jan 22 07:36:11 EST 2021

STATUS

proposed

reviewed

#7 by R. J. Mathar at Fri Jan 22 06:41:22 EST 2021

STATUS

editing

proposed

#6 by R. J. Mathar at Fri Jan 22 06:41:18 EST 2021

FORMULA

Equals (1/2)*Sum_{k>=2} 1/(k^4-1) - (1/2)*Sum_{k>=2} 1/(k^4+1) = (A256919-A256920)/2. - R. J. Mathar, Jan 22 2021

STATUS

approved

editing

#5 by Vaclav Kotesovec at Tue Dec 08 06:20:02 EST 2020

STATUS

editing

approved

#4 by Vaclav Kotesovec at Tue Dec 08 06:19:30 EST 2020

MATHEMATICA

Join[{0, 0}, RealDigits[15/16 - Pi*Coth[Pi]/8 + Pi*(Sin[Sqrt[2]*Pi] + Sinh[Sqrt[2]*Pi]) / (4*Sqrt[2]*(Cos[Sqrt[2]*Pi] - Cosh[Sqrt[2]*Pi])), 10, 100][[1]]]

#3 by Vaclav Kotesovec at Tue Dec 08 06:12:42 EST 2020

FORMULA

Equals Sum_{k>=2} 1/(k^8 - 1).

Equals 15/16 - Pi*coth(Pi)/8 + Pi * (sin(sqrt(2)*Pi) + sinh(sqrt(2)*Pi)) / (4*sqrt(2) * (cos(sqrt(2)*Pi) - cosh(sqrt(2)*Pi))).

MATHEMATICA

Equals Sum_{k>=2} 1/(k^8 - 1).

Equals 15/16 - Pi*coth(Pi)/8 + Pi * (sin(sqrt(2)*Pi) + sinh(sqrt(2)*Pi)) / (4*sqrt(2) * (cos(sqrt(2)*Pi) - cosh(sqrt(2)*Pi))).

#2 by Vaclav Kotesovec at Tue Dec 08 06:02:14 EST 2020

NAME

allocated for Vaclav KotesovecDecimal expansion of Sum_{k>=1} (zeta(8*k)-1).

DATA

0, 0, 4, 0, 9, 2, 6, 9, 8, 2, 9, 9, 2, 8, 6, 2, 8, 7, 3, 0, 7, 4, 7, 6, 2, 0, 4, 6, 8, 9, 6, 4, 0, 2, 5, 9, 8, 6, 5, 2, 4, 9, 8, 2, 4, 7, 3, 5, 4, 0, 0, 1, 6, 9, 8, 1, 2, 4, 9, 1, 0, 5, 6, 0, 0, 5, 5, 5, 7, 2, 1, 3, 9, 8, 9, 5, 8, 1, 9, 3, 5, 8, 3, 5, 4, 4, 8, 8, 9, 4, 3, 5, 1, 8, 1, 9, 6, 9, 5, 1, 1, 5, 0, 3, 6

OFFSET

0,3

EXAMPLE

0.00409269829928628730747620468964025986524982473540016981249105600555721...

MATHEMATICA

Equals Sum_{k>=2} 1/(k^8 - 1).

Equals 15/16 - Pi*coth(Pi)/8 + Pi * (sin(sqrt(2)*Pi) + sinh(sqrt(2)*Pi)) / (4*sqrt(2) * (cos(sqrt(2)*Pi) - cosh(sqrt(2)*Pi))).

CROSSREFS

Cf. A024006, A256919, A339529.

KEYWORD

allocated

nonn,cons

AUTHOR

Vaclav Kotesovec, Dec 08 2020, following a suggestion of Artur Jasinski

STATUS

approved

editing

#1 by Vaclav Kotesovec at Tue Dec 08 06:00:01 EST 2020

NAME

allocated for Vaclav Kotesovec

KEYWORD

allocated

STATUS

approved