# Lagrangian formalism and its auxiliary conditions: special function equations and Bateman oscillators

@article{Musielak2019LagrangianFA, title={Lagrangian formalism and its auxiliary conditions: special function equations and Bateman oscillators}, author={Zdzislaw E. Musielak and Niyousha Davachi and Marialis Rosario-Franco}, journal={arXiv: Mathematical Physics}, year={2019} }

Lagrangian formalism is established for differential equations whose solutions are given by special functions of mathematical physics, and for differential equations that describe the Bateman damped harmonic oscillators. The basis for the formalism are standard and non-standard Lagrangians. In this paper, it is shown that for non-standard Lagrangians the calculus of variations must be amended by auxiliary conditions whose existence have profound implications on the validity of the Helmholtz…

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