A066035 -id:A066035 - cp's OEIS frontend

A066034 Second term in the continued fraction expansion of StieltjesGamma[n].

1, -13, -103, 486, 430, 1260, -4188, -1896, -2839, -29074, 4870, 3701, 5978, -36411, -4779, -3527, -5007, 38056, 3253, 1985, 2144, 9575, -1846, -803, -629, -930, 1522, 287, 156, 135, 281, -133, -38, -22, -19, -49, 13, 4, 2, 1, 4, -1, -1, -3, -5, -13, 1, 25, 1, 1, 1, -5, -5, -1, -2, -7, -3, 3, 2, 3, 3, 1, 1, -1

Offset: 0

Wouter Meeussen, Dec 12 2001

sign

StieltjesGamma[0] equals EulerGamma

			The continued fraction expansions of the first four unsigned StieltjesGamma[n], n=0..3, are {0,1,1,2,1,2,1,4,3,13,5,1}, {0,13,1,2,1,2,1,74,1,10,1,9}, {0,103,5,8,3,9,1,8,10,1,10,1},{0,486,1,8,2,4,2,1,1,3,1,2}

Cf. A002852, A066035, A066036.

Part[ #, 2 ]&/@Table[ ContinuedFraction[ StieltjesGamma[ n ]~N~24, 12 ], {n, 0, 64} ]

A066036 Continued fraction expansion of StieltjesGamma[1].

Original entry on oeis.org

0, 13, 1, 2, 1, 2, 1, 74, 1, 10, 1, 9, 2, 1, 3, 1, 4, 1, 6, 1, 1, 2, 84, 1, 108, 1, 20, 22, 2, 2, 1, 2, 2, 1, 7, 1, 66, 2, 1, 1, 2, 5, 1, 1, 2, 1, 1, 59, 1, 2, 1, 5, 19, 3, 3, 1, 5, 4, 4, 1, 1, 4, 2, 32

Offset: 0

Wouter Meeussen, Dec 12 2001

			StieltjesGamma[1] = -0.07281584548367672486058637587490131913773633833433...

Cf. A002852, A066034, A066035.

ContinuedFraction[Abs@StieltjesGamma[n]~N~100, 64]

contfrac(intnum(x=0, oo, (1/tanh(Pi*x)-1)*(x*log(1+x^2)-2*atan(x))/(2*(1+x^2)))) \\ Charles R Greathouse IV, Mar 10 2016

cp's OEIS Frontend

A066034 Second term in the continued fraction expansion of StieltjesGamma[n].

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