Remarks on Lubbock's summation formulae

Abstract: 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.