C. M. Bender and L. M. Bettencourt, Multiple-scale analysis of quantum systems, Phys. Rev. D, pp.7710-7723, 1996.

J. Pain, Commutation relations of operator monomials, J. Phys. A: Math. Theor, vol.46, 2013.

N. H. Mccoy, On Commutation Formulas in the Algebra of Quantum Mechanic, Transactions of the American Mathematical Society, pp.793-806, 1929.

H. B. Domingo and E. A. Galapon, Generalized Weyl transform for operator ordering: Polynomial functions in phase space, Journal of Mathematical Physics, vol.56, 2015.

M. Abramowitz and I. A. Stegun, Handbook of mathematical functions: with formulas, graphs, and mathematical tables, 1970.

E. Elizalde, Ten physical applications of spectral zeta functions, 1995.

F. W. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions, 2010.

C. Figuieira-de-morisson and A. Fring, Time evolution of non-Hermitian Hamiltonian systems, J. Phys. A: Math. Gen, vol.39, 2006.

A. Hodges and C. V. Sukumar, Bernoulli, Euler, permutations and quantum algebras, Proc. R. Soc. A, vol.463, pp.2401-2412, 2007.

A. Mostafazadeh, Pseudo-Hermiticity versus PT-Symmetry: the necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian, J. Math. Phys, vol.43, pp.205-214, 2002.

S. Roman, The umbral calculus, 1984.

I. M. Gessel, Applications of the classical umbral calculus, Algebra Universalis, vol.49, issue.4, pp.397-434, 2003.