A273051 Decimal expansion of the second moment of the reciprocal gamma distribution.

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

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.6 Fransén-Robinson constant, p. 262.

Links

Table of n, a(n) for n=1..101.

Steven R. Finch Errata and Addenda to Mathematical Constants p. 35.

Eric Weisstein's MathWorld Fransén-Robinson Constant

Wikipedia, Reciprocal gamma function

Formula

(1/I)*Integral_{x>=0} x^2/gamma(x) dx where I = Integral_{x>=0} 1/gamma(x) dx is the Fransén-Robinson constant.

Example

4.83648597463342689473636069232113892436851608107360722903294224216...

Mathematica

digits = 101;
I0 = NIntegrate[1/Gamma[x], {x, 0, Infinity}, WorkingPrecision -> digits + 5];
M2 = (1/I0) NIntegrate[x^2/Gamma[x], {x, 0, Infinity}, WorkingPrecision -> digits + 5];
RealDigits[M2, 10, digits][[1]]

Prog

(PARI) default(realprecision, 120); intnum(x=0, [[1], 1], x^2/gamma(x))/intnum(x=0, [[1], 1], 1/gamma(x)) \\ Vaclav Kotesovec, May 14 2016

Crossrefs

Cf. A058655, A273017.

Sequence in context: A362530 A065191 A229988 * A021678 A180594 A066199

Adjacent sequences: A273048 A273049 A273050 * A273052 A273053 A273054

Keyword

nonn,cons

Author

Jean-François Alcover, May 14 2016

Status

approved