A267316 Decimal expansion of the Dirichlet eta function at 5.

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

Offset: 0

Author

Ilya Gutkovskiy, Jan 13 2016

Keywords

• nonn
• cons

Examples

			1/1^5 - 1/2^5 + 1/3^5 - 1/4^5 + 1/5^5 - 1/6^5 + ... = 0.972119770446909305935655143553469532553513362...
		

Links

• OEIS Wiki, Euler's alternating zeta function
• Eric Weisstein's World of Mathematics, Dirichlet Eta Function
• Wikipedia, Dirichlet Eta Function

Crossrefs

Cf. A002162 (value at 1), A013663, A072691 (value at 2), A197070 (value at 3), A267315 (value at 4), A136676, A334604.

Programs

Mathematica

RealDigits[(15 Zeta[5])/16, 10, 120][[1]]

PARI

15*zeta(5)/16 \\ Michel Marcus, Feb 01 2016

Sage

s = RLF(0); s
RealField(110)(s)
for i in range(1, 10000): s += -((-1)^i/((i)^5))
print(s) # Terry D. Grant, Aug 05 2016

Formula

Equals Sum_{k > 0} (-1)^(k+1)/k^5 = (15*zeta(5))/16.

Equals Lim_{n -> infinity} A136676(n)/A334604(n). - Petros Hadjicostas, May 07 2020