التفاصيل البيبلوغرافية
| العنوان: |
Analytical expressions and recurrence relations for the Pn−1(t)−Pn+1(t) function, derivative and integral |
| المؤلفون: |
Piretzidis Dimitrios(), Sideris, Michael G., 1958-(https://viaf.org/viaf/2695139Test) |
| بيانات النشر: |
Springer |
| سنة النشر: |
2022 |
| المجموعة: |
Technical University of Crete: Institutional Repository / Πολυτεχνείο Κρήτης: Ιδρυματικό Αποθετήριο |
| مصطلحات موضوعية: |
Legendre polynomials, Orthogonal polynomials, Recurrence relation, Truncated filter kernel |
| الوصف: |
Summarization: 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. ; Presented on: Journal of Geodesy |
| نوع الوثيقة: |
article in journal/newspaper |
| اللغة: |
English |
| العلاقة: |
info:eu-repo/grantAgreement/EC/FP7/246686; http://purl.tuc.gr/dl/dias/6FAF00ED-845F-4C0E-A15B-03BC18424FCATest |
| الإتاحة: |
http://purl.tuc.gr/dl/dias/6FAF00ED-845F-4C0E-A15B-03BC18424FCATest |
| حقوق: |
info:eu-repo/semantics/openAccess ; Όροι χρήσης: Μη διαθέσιμο ; License: http://creativecommons.org/licenses/by/4.0Test/ |
| رقم الانضمام: |
edsbas.771310FB |
| قاعدة البيانات: |
BASE |
