A273017 Decimal expansion of the first moment of the reciprocal gamma distribution.

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

Offset

1,2

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..100.

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

Eric Weisstein's World of Mathematics, Fransén-Robinson Constant

Wikipedia, Reciprocal gamma function

Formula

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

Example

1.93456704214788472118371470436917892438217559226658848385544754...

Mathematica

digits = 100;
I0 = NIntegrate[1/Gamma[x], {x, 0, Infinity}, WorkingPrecision -> digits + 5];
M1 = (1/I0) NIntegrate[x/Gamma[x], {x, 0, Infinity}, WorkingPrecision -> digits + 5];
RealDigits[M1, 10, digits][[1]]

Prog

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

Crossrefs

Cf. A058655.

Sequence in context: A011011 A236100 A070634 * A222233 A021111 A242302

Adjacent sequences: A273014 A273015 A273016 * A273018 A273019 A273020

Keyword

nonn,cons

Author

Jean-François Alcover, May 13 2016

Status

approved