Remarks on Lubbock's summation formulae

The coefficients occurring in summation formulae of the Lubbock type are shown to be generalised Bernoulli polynomials which turn up in subdivision questions such as quantum field theory around a conical singularity and on spherical lunes. An image interpretation is made, generating functions are brought in and some trigonometric summations encountered. A formal Lubbock formula is introduced for a general delta operator.