一类超几何函数扰动级数的闭式和
Closed-form sums for some perturbation series involving hypergeometric functions
摘要：
Sum{n=1，infinity}（alpha/2）_n_2F_1（-n，b; gamma; y）/（n n！）被调查。对于α为正整数α = 1，2，3，. b --> infinity的极限情况，在y被x^2/b替换后，导致Sum{n=1，infinity}（alpha/2）_n_1F_1（-n; gamma; x^2）/（n n！）。这类级数出现在广义尖峰谐振子哈密顿量H = -（d/dx）^2 + Bx^2 + A/x^2 + lambda/x^alpha，x >=0，alpha，lambda > 0，A >= 0的波函数的一阶微扰修正中。这些结果对于尖峰谐振子哈密顿量H = -（d/dx）^2 + Bx^2 + lambda/x^alpha，x >= 0，alpha，lambda > 0的能量和波函数的微扰级数有直接的应用。
英文摘要：
Infinite series of the type Sum{n=1,infinity}(alpha/2)_n_2F_1(-n, b; gamma; y)/(n n!) are investigated. Closed-form sums are obtained for alpha a positive integer alpha=1,2,3, ... The limiting case of b --> infinity, after y is replaced with x^2/b, leads to Sum{n=1,infinity}(alpha/2)_n_1F_1(-n; gamma; x^2)/(n n!). This type of series appears in the first-order perturbation correction for the wavefunction of the generalized spiked harmonic oscillator Hamiltonian H = -(d/dx)^2 + Bx^2 + A/x^2 + lambda/x^alpha, x >=0, alpha, lambda > 0, A >= 0. These results have immediate applications to perturbation series for the energy and wave function of the spiked harmonic oscillator Hamiltonian H = -(d/dx)^2 + Bx^2 + lambda/x^alpha, x >= 0, alpha, lambda > 0.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
