On certain series involving Laguerre polynomials

In this paper, we find closed-form sums for the series ∑n=1∞(α2)nn1n!1F1(−n,γ,x2), where α>0. This type of series appears in the first-order perturbation correction for the wavefunction of the generalized spiked harmonic oscillator Hamiltonian H=−d2dx2+Bx2+Ax2+λxα, where 0≤x<∞, α,λ>0, A≥0.