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| URI | http://purl.tuc.gr/dl/dias/6FAF00ED-845F-4C0E-A15B-03BC18424FCA | - |
| Αναγνωριστικό | https://doi.org/10.1007/s00190-021-01518-4 | - |
| Αναγνωριστικό | https://link.springer.com/article/10.1007/s00190-021-01518-4 | - |
| Γλώσσα | en | - |
| Μέγεθος | 12 pages | en |
| Τίτλος | Analytical expressions and recurrence relations for the Pn−1(t)−Pn+1(t) function, derivative and integral | en |
| Δημιουργός | Piretzidis Dimitrios | en |
| Δημιουργός | Sideris, Michael G., 1958- | en |
| Εκδότης | Springer | en |
| Περίληψη | In this paper, we discuss some methods for the calculation of the Legendre polynomial difference Pn−1(t)−Pn+1(t). Such differences frequently appear when calculating the spherical harmonic coefficients of truncated spatial filters. By examining the relation between the Legendre polynomials and other classical orthogonal polynomials (i.e., Gegenbauer and Jacobi polynomials), we provide analytical expressions for Pn−1(t)−Pn+1(t) in terms of the latter. We also derive a recurrence relation that avoids the direct evaluation of the Legendre polynomials. Analogous analytical expressions and recurrence relations are provided for the calculation of the Pn−1(t)−Pn+1(t) derivative and integral. We show that these recurrence relations can be derived from a more general recurrence relation; thus, the former are special cases of the latter. The expressions given in this study can be useful for the more efficient calculation of truncated kernels in the spherical harmonic domain. We demonstrate the applicability of these new expressions for the Pellinen (i.e., rectangular) filter kernel that is regularly used in regional gravity field modeling. | en |
| Τύπος | Peer-Reviewed Journal Publication | en |
| Τύπος | Δημοσίευση σε Περιοδικό με Κριτές | el |
| Άδεια Χρήσης | http://creativecommons.org/licenses/by/4.0/ | en |
| Ημερομηνία | 2022-11-22 | - |
| Ημερομηνία Δημοσίευσης | 2021 | - |
| Θεματική Κατηγορία | Legendre polynomials | en |
| Θεματική Κατηγορία | Orthogonal polynomials | en |
| Θεματική Κατηγορία | Recurrence relation | en |
| Θεματική Κατηγορία | Truncated filter kernel | en |
| Βιβλιογραφική Αναφορά | D. Piretzidis and M. G. Sideris, “Analytical expressions and recurrence relations for the Pn−1(t)−Pn+1(t) function, derivative and integral,” J. Geod., vol. 95, no. 6, May 2021, doi: 10.1007/s00190-021-01518-4. | en |
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