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A346042
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Decimal expansion of Sum_{k>=0} 2^floor(k/2)/(k!^2).
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0
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2, 5, 6, 2, 7, 9, 3, 5, 3, 4, 7, 8, 3, 1, 8, 9, 4, 6, 1, 6, 0, 7, 6, 8, 1, 6, 4, 5, 1, 3, 8, 5, 7, 1, 3, 3, 5, 1, 5, 0, 8, 4, 9, 0, 6, 7, 8, 9, 2, 0, 6, 6, 1, 1, 9, 2, 2, 7, 8, 9, 6, 7, 9, 2, 8, 8, 8, 6, 8, 5, 3, 8, 7, 0, 8, 5, 7, 6, 4, 5, 8, 4, 9, 7, 2, 5, 5, 4, 1, 2, 4, 2, 5, 3, 1, 7, 5, 9, 5, 9
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OFFSET
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1,1
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COMMENTS
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This constant is irrational (Mingarelli, 2013).
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LINKS
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Table of n, a(n) for n=1..100.
Angelo B. Mingarelli, Abstract factorials, Notes on Number Theory and Discrete Mathematics, Vol. 19, No. 4 (2013), pp. 43-76 (see p. 62); arXiv preprint, arXiv:0705.4299 [math.NT], 2007-2012.
Eric Weisstein's World of Mathematics, Bessel Function of the First Kind.
Eric Weisstein's World of Mathematics, Modified Bessel Function of the First Kind.
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FORMULA
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Equals (1/4)*(2+sqrt(2)) * BesselI(0,2^(5/4)) + (1/4)*(2-sqrt(2)) * BesselJ(0, 2^(5/4)), where BesselJ is the Bessel function of the first kind, and BesselI is the modified Bessel function of the first kind.
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EXAMPLE
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2.56279353478318946160768164513857133515084906789206...
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MAPLE
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evalf(sum(2^floor(k/2)/k!^2, k=0..infinity), 140); # Alois P. Heinz, Jul 03 2021
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MATHEMATICA
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RealDigits[(1/4) * (2+Sqrt[2]) * BesselI[0, 2^(5/4)] + (1/4) * (2-Sqrt[2]) * BesselJ[0, 2^(5/4)], 10, 100][[1]]
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PROG
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(PARI) suminf(k=0, 2^floor(k/2)/(k!^2)) \\ Michel Marcus, Jul 02 2021
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CROSSREFS
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Cf. A001044, A016116.
Sequence in context: A103130 A159987 A143678 * A021800 A140862 A305210
Adjacent sequences: A346039 A346040 A346041 * A346043 A346044 A346045
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KEYWORD
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nonn,cons
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AUTHOR
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Amiram Eldar, Jul 02 2021
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STATUS
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approved
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