Bessel's Interpolation Formula

Formula:

f(u) = { f(0) + f(1) }  + ( u – 1 ) ∆f(0)

                  2                          2

    +   u(u – 1) { ∆² f(-1) + ∆² f(0) }

                2i                         2

+  u(u – 1) (u – ½) ∆³ f(-1)

             3i

+ u(u + 1)(u – 1)(u – 2) { ∆⁴f(-2) + ∆⁴f(-1) }

                 4i                               2

 +. . . . . . .  .   . .. .. .. . . . .. . . . . .