An Analytical Evaluation For The Integral Of Two Spherical Bessel Functions With An Additional Exponential And Polynomial Factor

2011/10/27 by R. Mehrem, Mehrem, R.
Mathematics · Physics and Astronomy · #Differential Equations and Boundary Problems #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Nuclear Theory (nucl-th) #math-ph #math.MP #nucl-th

paper · pdf · doi:10.48550/arxiv.1110.6147

7 Pages

arxiv created 2011/10/27 · openalex publication_date 2011/10/27 · arxiv updated 2011/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The integrals \threej\Llo\Llt\Llth 000 ∫₀^∞ r^\Llth+1 e^-αr j_\Llo(k₁r) j_\Llt(k₂r) dr and \threej\Llo\Llt\Llth 000 ∫₀^∞ r^\Llth+2 e^-αr j_\Llo(k₁r) j_\Llt(k₂r) dr are evaluated analytically. The result is a finite sum over the associated Legendre function of the second kind.

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