Perturbation expansions for the spiked harmonic oscillator and related series involving the gamma function

We study weak-coupling perturbation expansions for the ground-state energy of the Hamiltonian with the generalized spiked harmonic oscillator potentia l V(x) = Bx(2) + x(2)/A + x(alpha)/lambda, and also for the bottoms of the angular-momentum subspaces labelled by l = 0, 1,..., in N dimensions corres ponding to the spiked harmonic oscillator potential V(x) = x(2) + x(alpha)/ lambda, where alpha is a real positive parameter. A method of Znojil (Znoji l M 1993 J. Math. Phys. 34 4914) is then applied to obtain closed-form expr essions for the sums of some infinite series whose terms involve ratios and products of gamma functions.