A lower set of nodes is a subset of a grid that can be indexed by a lower set of indices. In order to apply the Lagrange interpolation formula, it is convenient to express the Lagrange fundamental polynomials as sums of few terms. We present such a formula for the Lagrange interpolation formula in two variables. In the general multidimensional case, we express the Lagrange fundamental polynomia...

The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...

The credit for introducing the geometry of Lagrange spaces and their subspaces goes to the famous Romanian geometer Miron 1 . He developed the theory of subspaces of a Lagrange space together with Bejancu 2 . Miron and Anastasiei 3 and Sakaguchi 4 studied the subspaces of generalized Lagrange spaces GL spaces in short . Antonelli and Hrimiuc 5, 6 introduced the concept of φ-Lagrangians and stud...

We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.