A385966 Decimal expansion of the value of the coefficient [x^5] 1/Gamma(x).
1, 6, 6, 5, 3, 8, 6, 1, 1, 3, 8, 2, 2, 9, 1, 4, 8, 9, 5, 0, 1, 7, 0, 0, 7, 9, 5, 1, 0, 2, 1, 0, 5, 2, 3, 5, 7, 1, 7, 7, 8, 1, 5, 0, 2, 2, 4, 7, 1, 7, 4, 3, 4, 0, 5, 7, 0, 4, 6, 8, 9, 0, 3, 1, 7, 8, 9, 9, 3, 8, 6, 6, 0, 5, 6, 4, 7, 4, 2, 4, 8, 3, 1, 9, 4, 7, 1, 9, 1, 4, 6, 5, 8, 0, 4, 1, 6, 2, 6, 6, 2, 3, 9, 5, 5, 9, 3, 4, 0, 5, 1, 2, 8
Offset: 0
Examples
0.16653861138229148950170079510210523571...
Links
- Paolo Xausa, Table of n, a(n) for n = 0..10000
- M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, 6.1.34.
- I. S. Gradsteyn, I. M. Ryzhik, Tables of Series and Products, Academic Press (2014) 8.321.2 gives recurrence.
- R. J. Mathar, Erratum to Exercise A4.2 in "An Introduction to the Theory of the Riemann Zeta Function", viXra:2507.0094 (2025)
- Simon Plouffe, Table up to c_15, (2004)
- J. W. Wrench, Concerning two series for the Gamma Function, Math. Comp. 22 (1968) 617-626, Table 5.
Programs
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Maple
(Pi^4-60*Pi^2*gamma^2+60*gamma^4+480*gamma*Zeta(3))/1440 ; evalf(%) ;
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Mathematica
First[RealDigits[(Pi^4 - 60*Pi^2*#^2 + 60*#^4 + 480*#*Zeta[3])/1440 & [EulerGamma], 10, 100]] (* or *) First[RealDigits[Module[{x}, SeriesCoefficient[1/Gamma[x], {x, 0, 5}]], 10, 100]] (* Paolo Xausa, Aug 08 2025 *)
Comments