Combining Newton and Lagrange interpolation, we give q-identities which generalize results of Van Hamme, Uchimura, Dilcher and Prodinger.

There are two natural Chern-Simons theories associated with the embedding of a three-dimensional surface in Euclidean space; one is constructed using the induced metric connection – it involves only the intrinsic geometry, the other is extrinsic and uses the connection associated with the gauging of normal rotations. As such, the two theories appear to describe very different aspects of the sur...

In this work we suggest a new approach to the determination of new identities for Bell’s polynomials, based on the Lagrange inversion formula, and the binomial sequences. This approach allows the easy recovery of known identities and deduction of some new identities including these polynomials.

Wilf stated that the Lagrange inversion formula (LIF) is a remarkable tool for solving certain kinds of functional equations, and at its best it can give explicit formulas where other approaches run into stone walls. Here we present the LIF combinatorially in the form of lattice paths, and apply it to the divisibility property of the coefficients of a formal power series expansion. For the LIF,...