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Abstract In this paper, we find closed-form sums for the series ∑ n = 1 ∞ ( α 2 ) n n 1 n ! 1 F 1 ( −… Click to show full abstract
Abstract In this paper, we find closed-form sums for the series ∑ n = 1 ∞ ( α 2 ) n n 1 n ! 1 F 1 ( − n , γ , x 2 ) , 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 = − d 2 d x 2 + B x 2 + A x 2 + λ x α , where 0 ≤ x ∞ , α , λ > 0 , A ≥ 0 .
Keywords:
laguerre polynomials;
series involving;
certain series;
series;
involving laguerre
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2017
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!