Infinite series involving special functions obtained using simple one-dimensional quantum mechanical problems
Year: 2025
Type: article
Abstract: In this paper certain classes of infinite sums involving special functions are evaluated analytically by application of basic quantum mechanical principles to simple models of half harmonic oscillator and a particle trapped inside an infinite potential well. The infinite sums ∑ n = 0 ∞ 2 2 n ( 2 n + 1 ) ! Γ 2 ( n + 3 2 ) [ 2 F 1 ( − n , ν + 2 2 ; 3 2 ; 1 2 ) ] 2 , ∑ n = 0 ∞ [ L ν 2 n + 1 − ν ( b 2 2 ) ] 2 b 4 n 2 2 n ( 2 n + 1 ) ! and ∑ n = 1 ∞
Institution: University of Novi Sad
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408177369