On certain series involving Laguerre polynomials

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• 作者：Bujar Xh. Fejzullahu ^{bujar.fejzullahu@uni-pr.edu}
• 关键词：Laguerre polynomials ; Confluent hypergeometric function ; Hypergeometric function
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：449
• 期：2
• 页码：1790-1796
• 全文大小：254 K
• 卷排序：449

文摘

In this paper, we find closed-form sums for the series ∑n=1∞(α2)nn1n!1F1(−n,γ,x2), where α>0α>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<∞0≤x<∞, α,λ>0α,λ>0, A≥0A≥0.