Abstract
A new method of evaluating overlap integrals involving orthogonal polynomials is proposed. The technique relies on purely algebraic manipulation of the associated recurrence coefficients. For a large class of polynomials and for sufficiently large orders, these coefficients can be written explicitly as Taylor series in terms of powers of ε = 1/n, where n is the polynomial order. Such decompositions are perfectly suited to the accurate numerical evaluation of integrals involving high-order polynomials. Examples include the numerical evaluation of integrals involving classical orthogonal polynomials such as Laguerre, Jacobi, and Gegenbauer. © 2009 Society for Industrial and Applied Mathematics.
Original language | English |
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Pages (from-to) | 3884-3904 |
Number of pages | 20 |
Journal | SIAM Journal on Scientific Computing |
Volume | 31 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2009 |
Keywords
- Asymptotic expansion of integrals
- Orthogonal polynomial
- Quasi-classical approximation
- Transition matrix