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A336987
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Decimal expansion of Sum_{n>=2} sqrt(n)^log(n)/log(n)^sqrt(n).
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0
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3, 2, 2, 1, 9, 4, 1, 9, 5, 8, 4, 2, 4, 3, 3, 6, 5, 1, 5, 2, 4, 3, 5, 9, 3, 6, 1, 1, 7, 7, 2, 2, 8, 8, 4, 3, 9, 9, 1, 2, 3, 9, 0, 2, 7, 3, 6, 7, 0, 7, 8, 1, 7, 7, 8, 5, 7, 9, 3, 4, 2, 6, 1, 0, 3, 8, 2, 9, 5, 4, 1, 8, 3, 2, 7, 5, 3, 5, 9, 7, 1, 0, 4, 3, 4, 7, 7, 8, 3, 1, 7, 0, 6, 5, 9, 1, 1, 3, 9, 7
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OFFSET
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2,1
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COMMENTS
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The series u(n) = sqrt(n)^log(n)/log(n)^sqrt(n) is convergent because n^2 * u(n) -> 0 when n -> oo.
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REFERENCES
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J. Moisan & A. Vernotte, Analyse, Topologie et Séries, Exercices corrigés de Mathématiques Spéciales, Ellipses, 1991, Exercice B-1 a-3 pp. 70, 87-88.
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LINKS
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FORMULA
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Equals Sum_{n>=2} sqrt(n)^log(n)/log(n)^sqrt(n).
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EXAMPLE
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32.219419584243365152435936117722884...
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MAPLE
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evalf(sum(sqrt(n)^log(n)/log(n)^sqrt(n), n=2..infinity), 120);
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PROG
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(PARI) default(realprecision, 100); sumpos(n=2, sqrt(n)^log(n)/log(n)^sqrt(n)) \\ Michel Marcus, Aug 10 2020
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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