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 A329087 Decimal expansion of Sum_{k>=1} 1/(k^2-5), negated. 13
 6, 6, 6, 8, 3, 2, 5, 9, 5, 6, 6, 2, 7, 4, 4, 8, 5, 2, 9, 8, 2, 9, 6, 3, 3, 3, 9, 7, 6, 6, 9, 6, 8, 1, 5, 7, 5, 4, 3, 4, 3, 2, 5, 6, 6, 2, 3, 8, 0, 3, 9, 6, 4, 0, 4, 0, 5, 8, 3, 3, 4, 5, 8, 2, 7, 1, 4, 8, 6, 8, 3, 3, 7, 2, 8, 9, 9, 0, 6, 0, 3, 4, 3, 6, 8, 6, 0, 4, 9, 2, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS In general, for complex numbers z, if we define F(z) = Sum_{k>=0} 1/(k^2+z), f(z) = Sum_{k>=1} 1/(k^2+z), then we have: F(z) = (1 + sqrt(z)*Pi*coth(sqrt(z)*Pi))/(2z), z != 0, -1, -4, -9, -16, ...; f(z) = (-1 + sqrt(z)*Pi*coth(sqrt(z)*Pi))/(2z), z != 0, -1, -4, -9, -16, ...; Pi^2/6, z = 0. Note that f(z) is continuous at z = 0. This sequence gives f(-5) (negated). This and A329080 are essentially the same, but both sequences are added because some people may search for this, and some people may search for A329080. LINKS FORMULA Sum_{k>=1} 1/(k^2-5) = (-1 + (sqrt(-5)*Pi)*coth(sqrt(-5)*Pi))/(-10) = (-1 + (sqrt(5)*Pi)*cot(sqrt(5)*Pi))/(-10). EXAMPLE Sum_{k>=1} 1/(k^2-5) = -0.66683259566274485298... PROG (PARI) default(realprecision, 100); my(f(x) = (-1 + (sqrt(x)*Pi)/tanh(sqrt(x)*Pi))/(2*x)); f(-5) CROSSREFS Cf. A329080 (F(-5)), A329081 (F(-3)), A329082 (F(-2)), A113319 (F(1)), A329083 (F(2)), A329084 (F(3)), A329085 (F(4)), A329086 (F(5)). Cf. this sequence (f(-5)), A329088 (f(-3)), A329089 (f(-2)), A013661 (f(0)), A259171 (f(1)), A329090 (f(2)), A329091 (f(3)), A329092 (f(4)), A329093 (f(5)). Sequence in context: A098537 A276861 A131703 * A135357 A322346 A322345 Adjacent sequences:  A329084 A329085 A329086 * A329088 A329089 A329090 KEYWORD nonn,cons AUTHOR Jianing Song, Nov 04 2019 STATUS approved

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Last modified January 17 20:36 EST 2020. Contains 330987 sequences. (Running on oeis4.)