A250129 Decimal expansion of the negated value of the digamma function at 1/8.

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

Offset: 1

Author

Jean-François Alcover, Jan 15 2015

Keywords

• nonn
• cons
• easy

Examples

			Psi(1/8) = -8.388492663295854867802742923086343000051446...
		

Links

• Eric Weisstein's MathWorld, Gauss's Digamma Theorem.
• Wikipedia, Digamma function: special values.
• Index entries for sequences related to the digamma function

Crossrefs

Cf. A020759, A020777, A047787, A200064, A222457, A222458.

Programs

Mathematica

RealDigits[PolyGamma[1/8], 10, 105] // First

PARI

-psi(1/8) \\ Charles R Greathouse IV, Jan 15 2015

Formula

Psi(1/8) = -gamma - (1/2)*(1+sqrt(2))*Pi - sqrt(2)*arccoth(sqrt(2)) - 4*log(2).