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A247377
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Decimal expansion of Integral_{0..oo} 1/Gamma(1+x) dx, a variation of the Fransén-Robinson constant.
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1
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2, 2, 6, 6, 5, 3, 4, 5, 0, 7, 6, 9, 9, 8, 4, 8, 8, 3, 5, 0, 7, 1, 9, 6, 3, 8, 5, 7, 6, 7, 8, 2, 2, 0, 9, 1, 8, 4, 0, 8, 8, 2, 9, 7, 1, 4, 2, 8, 0, 2, 2, 2, 1, 9, 3, 8, 6, 1, 0, 9, 3, 5, 5, 4, 4, 2, 9, 1, 8, 8, 9, 9, 7, 6, 9, 1, 3, 7, 5, 2, 8, 1, 0, 8, 5, 0, 9, 1, 0, 6, 9, 7, 4, 7, 9, 3, 4, 0, 6, 9, 5, 8, 8, 4
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OFFSET
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1,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.6 Fransén-Robinson constant, p. 263.
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LINKS
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FORMULA
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Also equals e - Integral_{-oo..oo} e^(-e^x)/(x^2 + Pi^2) dx (observed by Ramanujan).
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EXAMPLE
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2.266534507699848835071963857678220918408829714280222193861...
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MATHEMATICA
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NIntegrate[1/Gamma[1 + x], {x, 0, Infinity}, WorkingPrecision -> 104] // RealDigits // First
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PROG
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(Python)
from mpmath import *
mp.dps = 200
A247377 = [d for d in nstr(quad(lambda x:1/gamma(1+x), [0, inf]), n=mp.dps)[:-1] if d != '.'] # Chai Wah Wu, Sep 16 2014
(PARI)
localprec(100); intnum(x=0, [[1], 1], 1/gamma(1+x)) \\ Dumitru Damian, Oct 12 2023
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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