Search: a242909 -id:a242909
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A242910
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Decimal expansion of exp(sqrt(Pi/24)).
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+10
4
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1, 4, 3, 5, 9, 1, 2, 6, 3, 1, 6, 1, 1, 7, 7, 3, 1, 2, 4, 7, 7, 2, 2, 4, 7, 2, 4, 0, 2, 8, 9, 9, 6, 5, 4, 5, 0, 5, 9, 0, 9, 4, 3, 5, 6, 3, 2, 5, 6, 1, 1, 3, 1, 4, 6, 6, 8, 0, 0, 5, 8, 1, 9, 4, 7, 3, 5, 0, 3, 2, 5, 4, 8, 0, 4, 2, 8, 4, 7, 9, 0, 6, 1, 6, 2, 1, 3, 1, 8, 5, 4, 5, 7, 8, 0, 1, 7, 5, 8, 7
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 3.10 Kneser-Mahler polynomial constants p. 234.
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LINKS
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FORMULA
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Lim_(m->infinity) M(z_1 + (1 + z_2)*(1 + z_3)*...*(1 + z_m))^(1/sqrt(m)), where M is Mahler's measure for multivariate polynomials.
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EXAMPLE
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1.43591263161177312477224724028996545059...
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MAPLE
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MATHEMATICA
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RealDigits[Exp[Sqrt[Pi/24]], 10, 100] // First
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PROG
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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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A242908
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Decimal expansion of exp(7*zeta(3)/(2*Pi^2)).
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+10
3
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1, 5, 3, 1, 5, 4, 7, 0, 9, 6, 6, 8, 7, 4, 5, 7, 7, 7, 6, 6, 4, 0, 7, 7, 7, 8, 6, 5, 1, 3, 5, 8, 0, 2, 0, 6, 0, 2, 0, 1, 7, 8, 3, 3, 7, 6, 9, 0, 3, 6, 4, 8, 9, 9, 8, 8, 4, 5, 6, 2, 7, 8, 7, 1, 4, 2, 8, 8, 5, 1, 7, 5, 2, 7, 6, 9, 8, 6, 5, 6, 2, 0, 7, 8, 3, 8, 0, 2, 3, 7, 7, 6, 3, 8, 6, 3, 8, 5, 4, 1
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 3.10 Kneser-Mahler polynomial constants p. 234.
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LINKS
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FORMULA
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M(1 + x + y + z) where M is Mahler's measure for multivariate polynomials.
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EXAMPLE
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1.5315470966874577766407778651358020602...
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MATHEMATICA
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RealDigits[Exp[7*Zeta[3]/(2*Pi^2)], 10, 100] // First
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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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A244238
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Decimal expansion of K = exp(8*G/(3*Pi)), a Kneser-Mahler constant related to an asymptotic inequality involving Bombieri's supremum norm, where G is Catalan's constant. K can be evaluated as Mahler's generalized height measure of the bivariate polynomial (1+x+x^2+y)^2.
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+10
1
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2, 1, 7, 6, 0, 1, 6, 1, 3, 5, 2, 9, 2, 3, 7, 0, 4, 2, 6, 2, 3, 5, 1, 6, 0, 7, 6, 5, 7, 3, 2, 3, 2, 7, 3, 7, 1, 6, 7, 7, 3, 2, 6, 6, 1, 3, 7, 1, 5, 4, 2, 2, 2, 5, 5, 1, 6, 3, 7, 8, 9, 8, 2, 3, 2, 2, 0, 2, 2, 9, 6, 8, 2, 8, 7, 0, 1, 8, 0, 2, 6, 0, 0, 7, 6, 6, 8, 5, 5, 0, 9, 2, 8, 5, 3, 4, 2, 5, 3, 1, 1, 9
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.10 Kneser-Mahler polynomial constants, p. 234.
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LINKS
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EXAMPLE
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2.17601613529237042623516...
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MATHEMATICA
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RealDigits[Exp[8*Catalan/(3*Pi)], 10, 102] // First
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PROG
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(PARI) default(realprecision, 100); exp(8*Catalan/(3*Pi)) \\ G. C. Greubel, Aug 25 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Exp(8*Catalan(R)/(3*Pi(R))); // G. C. Greubel, Aug 25 2018
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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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