Abstract
A few important integrals involving the product of two universal associated Legendre polynomials , and x2a(1 - x2)-p-1, xb(1 ± x)-p-1 and xc(1 -x2)-p-1 (1 ± x) are evaluated using the operator form of Taylor's theorem and an integral over a single universal associated Legendre polynomial. These integrals are more general since the quantum numbers are unequal, i.e. l′ ≠ k′ and m′ ≠ n′ Their selection rules are also given. We also verify the correctness of those integral formulas numerically.
Original language | English |
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Pages (from-to) | 177-180 |
Number of pages | 4 |
Journal | Communications in Theoretical Physics |
Volume | 68 |
Issue number | 2 |
DOIs | |
State | Published - 1 Aug 2017 |
Keywords
- Taylor's theorem
- definite integrals
- parity
- universal associated Legendre polynomials