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A242402
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Decimal expansion of the smallest positive root of the equation J_0(t)*I_1(t)+I_0(t)*J_1(t) = 0 (with I_0, I_1, J_0 and J_1, Bessel functions).
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1
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3, 1, 9, 6, 2, 2, 0, 6, 1, 6, 5, 8, 2, 5, 4, 1, 0, 9, 3, 9, 8, 0, 5, 2, 7, 4, 0, 3, 4, 0, 3, 7, 2, 0, 3, 4, 1, 5, 9, 9, 0, 8, 1, 1, 1, 1, 6, 2, 0, 2, 2, 2, 0, 4, 6, 8, 4, 2, 2, 7, 0, 3, 6, 4, 2, 3, 2, 3, 3, 3, 1, 1, 7, 2, 9, 7, 6, 1, 5, 2, 4, 5, 1, 1, 2, 6, 2, 7, 0, 0, 2, 1, 7, 5, 2, 2, 0, 9, 6, 1
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OFFSET
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1,1
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COMMENTS
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"This [constant] is associated with the study of a vibrating, homogeneous plate clamped at the boundary [of the unit disk]." - Quoted from Steven R. Finch.
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 222.
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LINKS
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EXAMPLE
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3.196220616582541093980527403403720341599...
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MATHEMATICA
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FindRoot[BesselJ[0, t]*BesselI[1, t] + BesselI[0, t]*BesselJ[1, t] == 0, {t, 3}, WorkingPrecision -> 100][[1, 2]] // RealDigits[#, 10, 100]& // First
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PROG
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(PARI) solve(t=3, 4, besselj(0, t)*besseli(1, t)+besseli(0, t)*besselj(1, t)) \\ Charles R Greathouse IV, Oct 23 2023
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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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