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A197036
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Decimal expansion of the Modified Bessel Function I of order 0 at 1.
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15
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1, 2, 6, 6, 0, 6, 5, 8, 7, 7, 7, 5, 2, 0, 0, 8, 3, 3, 5, 5, 9, 8, 2, 4, 4, 6, 2, 5, 2, 1, 4, 7, 1, 7, 5, 3, 7, 6, 0, 7, 6, 7, 0, 3, 1, 1, 3, 5, 4, 9, 6, 2, 2, 0, 6, 8, 0, 8, 1, 3, 5, 3, 3, 1, 2, 1, 3, 5, 7, 5, 0, 1, 6, 1, 2, 2, 7, 7, 5, 4, 7, 0, 3, 9, 4, 8, 1, 8, 3, 5, 7, 1, 4, 7, 2, 8, 0, 1, 0, 1, 8, 7, 1, 0, 3, 6, 1, 3, 4, 6, 8
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OFFSET
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1,2
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LINKS
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FORMULA
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I_0(1) = Sum_{k>=0} 1/(4^k*k!^2) = Sum_{k>=0} 1/A002454(k).
Equals (1/Pi)*Integral_{t=0..Pi} exp(cos(t)) dt.
Equals exp(-1) * Sum_{k>=0} binomial(2*k,k)/(2^k*k!).
Equals e * Sum_{k>=0} (-1/2)^k * binomial(2*k,k)/k!. (End)
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EXAMPLE
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1.26606587775200833559824462521471753760767031135496...
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MAPLE
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BesselI(0, 1) ; evalf(%) ;
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MATHEMATICA
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RealDigits[BesselJ[0, I], 10, 120][[1]] (* Amiram Eldar, Jun 15 2023 *)
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PROG
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CROSSREFS
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Bessel function values: A334380 (J(0,1)), A334383 (J(0,sqrt(2)), A091681 (J(0,2)), this sequence (I(0,1)), A334381 (I(0,sqrt(2)), A070910 (I(0,2)).
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KEYWORD
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AUTHOR
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STATUS
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approved
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