A375506 Decimal expansion of the first derivative of the Dirichlet eta-function eta(s) at s=3/2.

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

Offset

0,2

Links

Table of n, a(n) for n=0..95.

Formula

Equals log(2)*zeta(3/2)/sqrt(2) +(1-1/sqrt(2))*zeta'(3/2) = Sum_{i>=1} (-1)^i*log(i)/i^(3/2).

Example

0.12867475083035719009595292991030137571142185354249...

Maple

s :=3/2 ; 2^(1-s)*log(2)*Zeta(s)+(1-2^(1-s))*Zeta(1, s) ; evalf(%) ;

Mathematica

RealDigits[DirichletEta'[3/2], 10, 120][[1]] (* Amiram Eldar, Aug 19 2024 *)

Crossrefs

Cf. A091812 (at s=1), A210593 (at s=2), A349220 (at s=3), A078434 (zeta(3/2)), A375503 (zeta'(3/2)).

Sequence in context: A368645 A019914 A065473 * A054029 A197589 A124356

Adjacent sequences: A375503 A375504 A375505 * A375507 A375508 A375509

Keyword

nonn,cons

Author

R. J. Mathar, Aug 18 2024

Status

approved