(15),
which may similarly be regarded as an extension of the theorem that, if n is a positive integer,
| un = u0 + nδu1/2 + | n (n − 1) | δ2 u0 + | (n + 1) n (n − 1) | δ3 u1/2 + ... |
| 2! | 3! |
(16).
There are other central-difference formulae besides those mentioned above; the general symbolical expression is
uθ = (cosh θhD + sinh θhD) u0
(17),
where
cosh ½hD = μ, sinh ½hD = ½δ