OFFSET
1,2
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]
PROG
(PARI) besseljzero'(0) \\ Charles R Greathouse IV, Oct 23 2023
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Vladimir Reshetnikov, Sep 19 2010
STATUS
approved