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A288095
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Decimal expansion of m(8) = Sum_{n>=0} 1/n!8, the 8th reciprocal multifactorial constant.
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10
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3, 9, 8, 9, 2, 4, 1, 2, 1, 2, 6, 9, 0, 1, 3, 6, 5, 4, 4, 1, 3, 3, 6, 4, 2, 1, 3, 4, 8, 0, 1, 9, 0, 9, 9, 4, 3, 8, 3, 5, 9, 2, 7, 3, 9, 2, 4, 5, 7, 6, 8, 1, 4, 8, 2, 6, 2, 0, 9, 5, 5, 6, 6, 5, 3, 0, 4, 1, 6, 4, 8, 8, 7, 6, 0, 5, 1, 5, 5, 1, 0, 8, 3, 8, 6, 2, 6, 1, 2, 0, 8, 0, 8, 0, 0, 6, 8, 4, 2, 3, 0, 7, 9
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OFFSET
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1,1
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LINKS
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FORMULA
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m(k) = (1/k)*exp(1/k)*(k + Sum_{j=1..k-1} (gamma(j/k) - gamma(j/k, 1/k)) where gamma(x) is the Euler gamma function and gamma(a,x) the incomplete gamma function.
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EXAMPLE
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3.9892412126901365441336421348019099438359273924576814826209556653...
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MATHEMATICA
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m[k_] := (1/k) Exp[1/k] (k + Sum[k^(j/k) (Gamma[j/k] - Gamma[j/k, 1/k]), {j, 1, k - 1}]); RealDigits[m[8], 10, 103][[1]]
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PROG
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(PARI) default(realprecision, 105); (1/8)*exp(1/8)*(8 + sum(k=1, 7, 8^(k/8)*(gamma(k/8) - incgam(k/8, 1/8)))) \\ G. C. Greubel, Mar 28 2019
(Magma) SetDefaultRealField(RealField(107)); (1/8)*Exp(1/8)*(8 + (&+[8^(k/8)*Gamma(k/8, 1/8): k in [1..7]])); // G. C. Greubel, Mar 28 2019
(Sage) numerical_approx((1/8)*exp(1/8)*(8 + sum(8^(k/8)*(gamma(k/8) - gamma_inc(k/8, 1/8)) for k in (1..7))), digits=105) # G. C. Greubel, Mar 28 2019
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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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