Special Lie–Mei Symmetry and Conserved Quantities of Appell Equations Expressed by Appell Fun

Special Lie–Mei symmetry and conserved quantities for Appell equations expressed by Appell functions in a holonomic mechanical system are investigated. On the basis of the Appell equation in a holonomic system, the definition and the criterion of special Lie–Mei symmetry of Appell equations expressed by Appell functions are given. The expressions of the determining equation of special Lie–Mei symmetry of Appell equations expressed by Appell functions, Hojman conserved quantity and Mei conserved quantity deduced from special Lie–Mei symmetry in a holonomic mechanical system are gained. An example is given to illustrate the application of the results.