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A267315 Decimal expansion of the Dirichlet eta function at 4. 4
9, 4, 7, 0, 3, 2, 8, 2, 9, 4, 9, 7, 2, 4, 5, 9, 1, 7, 5, 7, 6, 5, 0, 3, 2, 3, 4, 4, 7, 3, 5, 2, 1, 9, 1, 4, 9, 2, 7, 9, 0, 7, 0, 8, 2, 9, 2, 8, 8, 8, 6, 0, 4, 4, 2, 2, 2, 6, 0, 4, 1, 8, 8, 5, 1, 3, 6, 0, 5, 5, 3, 9, 1, 6, 3, 5, 9, 7, 7, 4, 0, 7, 3, 7, 2, 9, 5, 9, 3, 1, 4, 4, 8, 9, 8, 7, 4, 2, 7, 5, 7, 8, 8, 6, 6, 9, 6, 2, 1, 6, 9, 5, 3, 7, 3, 9, 9, 6, 1, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..119.

OEIS Wiki, Euler's alternating zeta function

Eric Weisstein's World of Mathematics, Dirichlet Eta Function

Wikipedia, Dirichlet Eta Function

FORMULA

Equals Sum_{k>0} -(-1)^k/k^4 = (7*Pi^4)/720.

EXAMPLE

1/1^4 - 1/2^4 + 1/3^4 - 1/4^4 + 1/5^4 - 1/6^4 + ... = 0.9470328294972459175765032344735219149279070829288860...

MATHEMATICA

RealDigits[(7 Pi^4)/720, 10, 120][[1]]

PROG

(PARI) 7*Pi^4/720 \\ Michel Marcus, Feb 01 2016

(MAGMA) pi:= 7*Pi(RealField(110))^4 / 720; Reverse(Intseq(Floor(10^100*pi))); // Vincenzo Librandi, Feb 04 2016

(Sage) s = RLF(0); s

RealField(110)(s)

for i in xrange(1, 10000): s += -((-1)^i/((i)^4))

print s # Terry D. Grant, Aug 04 2016

CROSSREFS

Cf. A002162, A072691, A197070.

Sequence in context: A245084 A199054 A131109 * A247412 A154397 A116186

Adjacent sequences:  A267312 A267313 A267314 * A267316 A267317 A267318

KEYWORD

nonn,cons

AUTHOR

Ilya Gutkovskiy, Jan 13 2016

STATUS

approved

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Last modified June 27 16:18 EDT 2017. Contains 288790 sequences.