Generalization of the Lagrange Expansion with Application to Physical Problems

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Abstract
Certain problems of fluid dynamics are conveniently discussed in the Lagrangian description by means of the displacement‐vector function. The Eulerian variables describing the motion may be obtained from the displacement‐vector function by a generalization of the Lagrange expansion which is here established. Two examples of the application of this expansion are given; the derivation of the Fokker‐Planck equation, and the description of the surface conditions of a rippling electron stream by the device of equivalent surface charges.