13/04/18 23:13:07.98
Let a be fine-structure constant.
a is given by the Hans-de-Vries (HdV) equation:
a = Γ(a)^2･exp(-ππ/2),
The Γ(a) factor is a small correction on the Gaussian exponential.
It can be expressed as a so-called radiative series in a.
(Hans de Vries, 2004/10/04）
Instead, we suppose Γ can be expressed by finite terms:
Γ(a) = 1 + 2π･sinh(a/2π) + aa/(2π),
then we get a = 1／137.035999075193･･･
Ｉ(x) is the modified Bessel function of the first kind. (1/2-th order)
Ｉ(x) = √(2/π)･sinh(x)/√x,
then, Γ(a) = 1 + (π√a)･Ｉ(a/2π) + aa/(2π),