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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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%I #6 Oct 23 2023 09:06:41

%S 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,

%T 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,

%U 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

%N 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).

%C "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.

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

%e 3.196220616582541093980527403403720341599...

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

%o (PARI) solve(t=3,4, besselj(0,t)*besseli(1,t)+besseli(0,t)*besselj(1,t)) \\ _Charles R Greathouse IV_, Oct 23 2023

%Y Cf. A115368.

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, May 13 2014