>>345
J_n の母関数定義　
e^{1/2z(t-1/t)} = Σ_{-∞ ≦< n < ∞} J_n(z) t^n
と e^{1/2z(t-1/t)}e^{1/2z(-t+1/t)}=1 より
1 = e^{1/2z(t-1/t)}e^{1/2z(-t+1/t)}=Σ_{-∞ < n, m < ∞} J_n(z) J_m t^{n+m} (-1)^m
=Σ_{-∞ < n < ∞} J_n(z) J_{-n} (-1}^n = J_0(Z) + 2 Σ_{1 ≦ n } J_n(z)^2