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A273051 Decimal expansion of the second moment of the reciprocal gamma distribution. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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: A248508 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

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Last modified July 29 15:22 EDT 2021. Contains 346346 sequences. (Running on oeis4.)