A242402 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).

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

Offset

1,1

Comments

"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.

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 222.

Links

Table of n, a(n) for n=1..100.

Example

3.196220616582541093980527403403720341599...

Mathematica

FindRoot[BesselJ[0, t]*BesselI[1, t] + BesselI[0, t]*BesselJ[1, t] == 0, {t, 3}, WorkingPrecision -> 100][[1, 2]] // RealDigits[#, 10, 100]& // First

Prog

(PARI) solve(t=3, 4, besselj(0, t)*besseli(1, t)+besseli(0, t)*besselj(1, t)) \\ Charles R Greathouse IV, Oct 23 2023

Crossrefs

Cf. A115368.

Sequence in context: A187537 A246256 A157393 * A217629 A127552 A229759

Adjacent sequences: A242399 A242400 A242401 * A242403 A242404 A242405

Keyword

nonn,cons

Author

Jean-François Alcover, May 13 2014

Status

approved