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A091659
Decimal expansion of (PolyGamma(1,(1+sqrt(5))/4)-PolyGamma(1,(3+sqrt(5))/4))/2.
3
5, 6, 8, 3, 0, 0, 0, 0, 3, 1, 4, 6, 2, 3, 5, 1, 7, 8, 7, 6, 0, 3, 3, 0, 4, 1, 1, 0, 3, 3, 1, 7, 5, 1, 5, 1, 4, 0, 7, 5, 2, 6, 6, 7, 4, 7, 8, 2, 5, 4, 0, 6, 1, 2, 2, 7, 2, 9, 5, 6, 7, 0, 5, 1, 8, 7, 7, 9, 2, 0, 8, 9, 7, 2, 4, 5, 9, 4, 0, 0, 2, 8, 0, 8, 2, 5, 7, 1, 4, 5, 4, 1, 5, 5, 2, 8, 5, 3, 2, 2, 7, 4
OFFSET
0,1
REFERENCES
S. R. Finch, Mathematical Constants, Cambridge, 2003, p. 424.
LINKS
Eric Weisstein's World of Mathematics, Ramanujan Continued Fractions
EXAMPLE
0.568300003...
MATHEMATICA
4*Integrate[(x*Sech[x])/E^(Sqrt[5]*x), {x, 0, Infinity}]
RealDigits[(PolyGamma[1, (1+Sqrt[5])/4]-PolyGamma[1, (3+Sqrt[5])/4])/2, 10, 100][[1]] (* Vaclav Kotesovec, Aug 16 2015 *)
PROG
(PARI)
polygamma(n, x) = if (n == 0, psi(x), (-1)^(n+1)*n!*zetahurwitz(n+1, x));
(polygamma(1, (1+sqrt(5))/4) - polygamma(1, (3+sqrt(5))/4))/2 \\ Gheorghe Coserea, Sep 30 2018
CROSSREFS
Cf. A091660.
Sequence in context: A337711 A345411 A275480 * A271571 A349577 A094931
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jan 26 2004
STATUS
approved