A175838 Let rho(n) be the first positive root of Bessel function J_n(x). This sequence is decimal expansion of derivative rho'(0)=1.54288974...

1, 5, 4, 2, 8, 8, 9, 7, 4, 2, 5, 9, 9, 3, 1, 3, 6, 8, 8, 0, 7, 0, 3, 2, 1, 4, 2, 1, 4, 7, 1, 4, 3, 5, 5, 6, 1, 6, 9, 8, 4, 6, 0, 7, 8, 7, 3, 5, 0, 1, 9, 7, 5, 8, 9, 3, 5, 2, 5, 2, 9, 4, 4, 1, 0, 2, 6, 8, 2, 5, 6, 4, 6, 9, 7, 2, 9, 1, 1, 2, 6, 0, 5, 0, 2, 3, 8, 2, 7, 4, 6, 7, 3, 8, 1, 0, 4, 7, 5, 6, 6, 1, 5, 4, 6

Offset: 1

Author

Vladimir Reshetnikov, Sep 19 2010

Keywords

• cons
• nonn

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A115368. - R. J. Mathar, Sep 22 2010

Programs

Maple

From R. J. Mathar, Sep 22 2010: (Start)
Digits := 120 : Jnudnu := proc(nu,z,kmax) -add( (-1)^k*Psi(nu+k+1)/GAMMA(nu+k+1)*(z/2)^(2*k+nu)/k! , k=0..kmax) ; evalf(%) ; end proc:
Jprime := diff(BesselJ(0,x),x) ; z := evalf(BesselJZeros(0,1)) ; denomin := subs(x=z,Jprime) ;
for kmax from 30 to 70 by 10 do numerat := Jnudnu(0,z,kmax) ; c := evalf(-numerat/denomin) ; print(c) ; end do: # Abramowitz-Stegun 9.1.64
(End)

Mathematica

N[(Pi BesselY[0,BesselJZero[0,1]])/(2 BesselJ[1,BesselJZero[0,1]]),200]

PARI

besseljzero'(0) \\ Charles R Greathouse IV, Oct 23 2023