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A143624 Decimal expansion of the negated constant cos(1) - sin(1) = -0.3011686789... 7
3, 0, 1, 1, 6, 8, 6, 7, 8, 9, 3, 9, 7, 5, 6, 7, 8, 9, 2, 5, 1, 5, 6, 5, 7, 1, 4, 1, 8, 7, 3, 2, 2, 3, 9, 5, 8, 9, 0, 2, 5, 2, 6, 4, 0, 1, 8, 0, 4, 4, 8, 8, 3, 8, 0, 0, 2, 6, 5, 4, 4, 5, 4, 6, 1, 0, 8, 1, 0, 0, 0, 9, 6, 1, 6, 7, 6, 7, 9, 0, 4, 4, 3, 0, 6, 8, 7, 8, 8, 7, 4, 5, 5, 8, 6, 9, 6, 0, 6, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

cos(1) - sin(1) = Sum_{n>=0} (-1)^floor(n/2)*n/n! = 1/1! - 2/2! - 3/3! + 4/4! + 5/5! - 6/6! - 7/7! + + - - ... . Define E_2(k) = Sum_{n>=0} (-1)^floor(n/2)*n^k/n! for k = 0,1,2,... . Then E_2(1) = cos(1) - sin(1) and E_2(0) = cos(1) + sin(1). Furthermore, E_2(k) is an integral linear combination of E_2(0) and E_2(1) (a Dobinski-type relation). For example, E_2(2) = E_2(1) - E_2(0), E_2(3) = -3*E_2(0) and E_2(4) = -5*E_2(1) - 6*E_2(0). The precise result is E_2(k) = A121867(k) * E_2(0) - A121868(k) * E_2(1). The decimal expansion of the constant cos(1) + sin(1) is recorded in A143623. Compare with A143625.

LINKS

Table of n, a(n) for n=0..99.

Eric Weisstein's World of Mathematics, Spherical Bessel Function of the First Kind

FORMULA

sin(1-Pi/4)*sqrt(2). - Franklin T. Adams-Watters, Jun 27 2014

Equals j_1(1), where j_1(z) is the spherical Bessel function of the first kind. - Stanislav Sykora, Jan 11 2017

EXAMPLE

cos(1) - sin(1) = -0.30116867893975678925156571418732239589025264018...

CROSSREFS

Cf. A049469, A049470, A057077, A121867, A121868, A143623, A143625.

Sequence in context: A011256 A220691 A271023 * A126308 A094923 A160499

Adjacent sequences:  A143621 A143622 A143623 * A143625 A143626 A143627

KEYWORD

cons,easy,nonn

AUTHOR

Peter Bala, Aug 30 2008

EXTENSIONS

Added sign in definition. Offset corrected by R. J. Mathar, Feb 05 2009

STATUS

approved

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Last modified June 22 12:17 EDT 2017. Contains 288613 sequences.