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A245261
Decimal expansion of the maximum of Planck's radiation function.
1
3, 2, 6, 4, 8, 0, 3, 4, 3, 3, 9, 7, 5, 5, 5, 7, 1, 4, 0, 2, 2, 8, 8, 1, 3, 1, 1, 9, 8, 5, 5, 7, 6, 3, 8, 2, 7, 8, 9, 8, 2, 7, 6, 1, 8, 7, 1, 3, 8, 5, 3, 6, 1, 9, 5, 8, 9, 5, 6, 9, 5, 6, 0, 9, 3, 8, 8, 1, 3, 9, 2, 5, 7, 3, 1, 5, 5, 5, 1, 5, 7, 1, 1, 8, 4, 8, 5, 4, 2, 8, 2, 0, 4, 4, 0, 5, 7, 8, 5, 7, 8, 6, 3, 1, 5
OFFSET
1,1
FORMULA
(15*(W(-(5/e^5)) + 5)^5)/((-1 + exp(W(-(5/e^5)) + 5))*Pi^4), where W is the LambertW function (also known as ProductLog).
EXAMPLE
3.2648034339755571402288131198557638278982761871385361958956956...
MATHEMATICA
f[x_] := 15/(Pi^4*x^5*(Exp[1/x] - 1)); xmax = 1/(ProductLog[-5*Exp[-5]] + 5); RealDigits[f[xmax], 10, 105] // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved