A note on generating functions and summation formulae for Meixner polynomials of several variables
Abstract The present paper deals with certain generating functions and various elegant summation formulae for Meixner polynomials of several variables.
Some generalizations of the Euler-Knopp transformation
SummaryThe purpose of this paper is to construct a generalization of the Euler-Knopp transformation. Using this, one may recover previously known transformations, derive new transformations useful for numerical calculations and derive generating functions and other formulas of theoretical interest involving well-known functions.
Three-dimensional elasticity problems for the prismatic bar
A general solution is given to the three-dimensional linear elastic problem of a prismatic bar subjected to arbitrary tractions on its lateral surfaces, subject only to the restriction that they can be expanded as finite power series in the axial coordinate z. The solution is obtained by repeated differentiation of the tractions with respect to z, establishing a set of sub-problems . A recursive procedure is then developed for generating the solution to from that for . This procedure involves three steps: integration of the stress and displacement fields with respect to z, using an appropriate Papkovich–Neuber (P–N) representation; solution of two-dimensional in-plane and antiplane corrective problems for the tractions in that are independent of z; and expression of these corrective solutions in P–N form. The method is illustrated by an example.