{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T06:36:57Z","timestamp":1776753417000,"version":"3.51.2"},"reference-count":46,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2013,5]]},"abstract":"<jats:p>Morais has recently introduced certain complete orthogonal sets of monogenic polynomials over 3D prolate spheroids with remarkable properties. The underlying functions take on either values in the reduced and full quaternions (identified, respectively, with \u211d<jats:sup>3<\/jats:sup>and \u211d<jats:sup>4<\/jats:sup>), and are generally assumed to be nullsolutions of the well known Riesz and Moisil\u2013Th\u00e9odoresco systems in \u211d<jats:sup>3<\/jats:sup>. In continuation of these studies, we recall some fundamental properties of the polynomials, and prove some recursive formulae between them. As a consequence, we obtain a two-term type recurrence relation satisfied by those basis polynomials. These results are then employed to investigate a rather wide class of approximation properties for monogenic functions over 3D prolate spheroids in terms of spheroidal monogenics.<\/jats:p>","DOI":"10.1142\/s0219691313500240","type":"journal-article","created":{"date-parts":[[2013,6,5]],"date-time":"2013-06-05T06:59:38Z","timestamp":1370415578000},"page":"1350024","source":"Crossref","is-referenced-by-count":7,"title":["ON CONVERGENCE PROPERTIES OF 3D SPHEROIDAL MONOGENICS"],"prefix":"10.1142","volume":"11","author":[{"given":"J.","family":"MORAIS","sequence":"first","affiliation":[{"name":"Centro de Investiga\u00e7\u00e3o e Desenvolvimento em Matem\u00e1tica e Aplica\u00e7\u00f5es (CIDMA), Universidade de Aveiro, 3810-193 Aveiro, Portugal"}]},{"given":"K. I.","family":"KOU","sequence":"additional","affiliation":[{"name":"Faculty of Science and Technology, University of Macau, Macau"}]},{"given":"S.","family":"GEORGIEV","sequence":"additional","affiliation":[{"name":"Department of Differential Equations, University of Sofia, Sofia, Bulgaria"}]}],"member":"219","published-online":{"date-parts":[[2013,6,4]]},"reference":[{"key":"rf1","volume-title":"Boundary Value Problems for Second-Order Elliptic Equations","author":"Bitsadze A.","year":"1968"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.1033"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2004.03.010"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1080\/17476930600689084"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-010-9411-z"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903432425"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/s00006-010-0262-4"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1080\/17476930701466630"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/BF03321722"},{"key":"rf12","volume-title":"Spheroidal Wave Functions","author":"Flammer C.","year":"1957"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01202702"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1953.3.585"},{"key":"rf16","doi-asserted-by":"crossref","DOI":"10.1515\/9783112576182","volume-title":"Quaternionic Analysis and Elliptic Boundary Value Problems","author":"G\u00fcrlebeck K.","year":"1989"},{"key":"rf17","volume-title":"Quaternionic Calculus for Engineers and Physicists","author":"G\u00fcrlebeck K.","year":"1997"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(97)00066-9"},{"key":"rf19","volume-title":"Holomorphic Functions in the Plane and n-dimensional Space","author":"G\u00fcrlebeck K.","year":"2008"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84996-108-0_16"},{"key":"rf22","volume-title":"The Theory of Spherical and Ellipsoidal Harmonics","author":"Hobson E.","year":"1931"},{"key":"rf23","author":"Kou K. 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