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A256501
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Decimal expansion of the positive solution to x = 4*(1-exp(-x)).
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4
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3, 9, 2, 0, 6, 9, 0, 3, 9, 4, 8, 7, 2, 8, 8, 6, 3, 4, 3, 5, 6, 0, 8, 9, 1, 3, 5, 2, 6, 1, 3, 5, 3, 6, 2, 2, 0, 5, 2, 5, 6, 2, 7, 3, 7, 1, 2, 0, 7, 9, 8, 4, 5, 3, 0, 4, 0, 1, 1, 7, 5, 0, 0, 5, 7, 9, 0, 5, 0, 5, 6, 4, 8, 3, 6, 6, 7, 0, 5, 7, 5, 7, 4, 3, 3, 6, 5, 6, 6, 0, 1, 8, 9, 4, 8, 3, 6, 5, 8, 9, 0, 4, 7, 3, 0
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OFFSET
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1,1
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COMMENTS
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Each of the positive solutions to x = q*(1-exp(-x)) obtained for q = 2, 3, 4, and 5, appears in several formulas pertinent to Planck's black-body radiation law. For a given q, the solution can be also written as q+W(-q/exp(q)), where W is the Lambert function. Here q = 4.
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LINKS
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EXAMPLE
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3.9206903948728863435608913526135362205256273712079845304011750...
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MATHEMATICA
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RealDigits[x/.FindRoot[x==4(1-Exp[-x]), {x, 3}, WorkingPrecision->120]] [[1]] (* Harvey P. Dale, May 08 2017 *)
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PROG
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(PARI) a4=solve(x=0.1, 10, x-4*(1-exp(-x))) \\ Use real precision in excess
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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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