

A249022


Decimal expansion of Sine Euler constant.


1



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

0,1


COMMENTS

The Sine Euler constant is introduced here as the limit as n increases without bound of sum{sin(1/k), k = 1..n}  integral{sin(1/x) over [1,n]}; this is analogous to the Euler constant, defined as the limit of sum{1/k, k = 1..n}  integral{1/x over [1,n]}.


LINKS

Table of n, a(n) for n=0..26.


EXAMPLE

Sine Euler constant = 0.466599306203729265221734220...


MATHEMATICA

f = DifferenceRoot[Function[{\[FormalY], \[FormalN]}, {((2 \[FormalN]  z) (2 \[FormalN]  (z + 1))) \[FormalY][\[FormalN]] + \[FormalY][1 + \[FormalN]] == 0, \[FormalY][1] == 1}]];
(Total[Table[1/((1)^(n + 1) (2 n  1)!) HarmonicNumber[k, 2 n  1], {n, 50}]] /. k > #)  (CosIntegral[1]  CosIntegral[1/#]  Sin[1] + # Sin[1/#]) &[N[10^35, 40]]
RealDigits[t][[1]]
(* Peter J. C. Moses, Oct 20 2014 *)


CROSSREFS

Cf. A001620 (Euler constant), A249023 (Tangent Euler constant).
Sequence in context: A155907 A081261 A251738 * A270541 A046262 A147862
Adjacent sequences: A249019 A249020 A249021 * A249023 A249024 A249025


KEYWORD

nonn,easy,cons


AUTHOR

Clark Kimberling, Oct 22 2014


STATUS

approved



