{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T11:25:31Z","timestamp":1777461931838,"version":"3.51.4"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2012,8,21]],"date-time":"2012-08-21T00:00:00Z","timestamp":1345507200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Methods Funct. Theory"],"published-print":{"date-parts":[[2012,12]]},"DOI":"10.1007\/bf03321840","type":"journal-article","created":{"date-parts":[[2013,4,3]],"date-time":"2013-04-03T04:19:55Z","timestamp":1364962795000},"page":"501-515","source":"Crossref","is-referenced-by-count":14,"title":["Generalized Derivative and Primitive of Cliffordian Bases of Polynomials Constructed Through Appell Monomials"],"prefix":"10.1007","volume":"12","author":[{"given":"Mohra","family":"Zayed","sequence":"first","affiliation":[]},{"given":"Mahmoud","family":"Abul-Ez","sequence":"additional","affiliation":[]},{"given":"Jo\u00e3o Pedro","family":"Morais","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,8,21]]},"reference":[{"issue":"1-4","key":"BF03321840_CR1","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1080\/17476939008814416","volume":"14","author":"M Abul-Ez","year":"1990","unstructured":"M. Abul-Ez and D. Constales, Basic sets of polynomials in Clifford analysis, Complex Variables 14 no.1-4(1990), 177\u2013185.","journal-title":"Complex Variables"},{"issue":"2","key":"BF03321840_CR2","first-page":"143","volume":"48","author":"M Abul-Ez","year":"1991","unstructured":"M. Abul-Ez and D. Constales, Linear substitution for basic sets of polynomials in Clifford analysis, Port. Math. 48 no.2 (1991), 143\u2013154.","journal-title":"Port. Math."},{"issue":"5","key":"BF03321840_CR3","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1007\/s00013-003-0490-0","volume":"80","author":"M Abul-Ez","year":"2003","unstructured":"M. Abul-Ez and D. Constales, The square root base of polynomials in Clifford analysis, Arch. Math 80 no.5 (2003), 486\u2013495.","journal-title":"Arch. Math"},{"issue":"1","key":"BF03321840_CR4","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1007\/s00013-003-4670-8","volume":"81","author":"M Abul-Ez","year":"2002","unstructured":"M. Abul-Ez and D. Constales, On convergence properties of basic series representing special monogenic functions, Arch. Math. 81 no.1 (2002), 62\u201371.","journal-title":"Arch. Math."},{"issue":"3","key":"BF03321840_CR5","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1002\/mma.1176","volume":"33","author":"L Aloui","year":"2009","unstructured":"L. Aloui and G. Hassan, Hypercomplex derivative bases of polynomials in Clifford analysis, Math. Methods Appl. Sci. 33 no.3 (2009), 350\u2013357.","journal-title":"Math. Methods Appl. Sci."},{"key":"BF03321840_CR6","doi-asserted-by":"crossref","unstructured":"P. Appell, Sur une classe de p\u00f4lynomes, Ann. Sci. Ecole Norm. Sup. (9) 21 (1880).","DOI":"10.24033\/asens.186"},{"issue":"4","key":"BF03321840_CR7","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1002\/mma.1213","volume":"33","author":"S Bock","year":"2009","unstructured":"S. Bock and K. G\u00fcrlebeck, On a generalized Appell system and monogenic power series, Math. Methods Appl. Sci. 33 no.4 (2009), 394\u2013411.","journal-title":"Math. Methods Appl. Sci."},{"key":"BF03321840_CR8","volume-title":"Clifford Analysis","author":"F Brackx","year":"1982","unstructured":"F. Brackx, R. Delanghe and F. Sommen, Clifford Analysis, Pitman, Boston, London, Melbourne, 1982."},{"key":"BF03321840_CR9","unstructured":"I. Ca\u00e7\u00e3o, Constructive approximation by monogenic polynomials, Ph.D. thesis, Universidade de Aveiro, 2004."},{"issue":"2-3","key":"BF03321840_CR10","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s11075-010-9411-z","volume":"55","author":"I Ca\u00e7\u00e3o","year":"2010","unstructured":"I. Ca\u00e7\u00e3o, Complete orthonormal sets of polynomial solutions of the Riesz and Moisil-Teodorescu systems in \u211d3, Numer. Algor. 55 no.2-3 (2010), 191\u2013203.","journal-title":"Numer. Algor."},{"key":"BF03321840_CR11","first-page":"647","volume-title":"Numerical Analysis and Applied Mathematics, AIP Conference Proceedings 1048","author":"I Ca\u00e7\u00e3o","year":"2008","unstructured":"I. Ca\u00e7\u00e3o and H. Malonek, On complete sets of hypercomplex Appell polynomials, in: T.E. Simos, G. Psihoyios, Ch. Tsitouras (eds.), Numerical Analysis and Applied Mathematics, AIP Conference Proceedings 1048, American Institute of Physics: Melville, NY, (2008), 647\u2013650."},{"issue":"2","key":"BF03321840_CR12","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s00013-006-1790-y","volume":"88","author":"D Constales","year":"2007","unstructured":"D. Constales, R. De Almeida and R. S. Krau\u00dfhar, On the growth type of entire monogenic functions, Arch. Math. 88 no.2 (2007), 153\u2013163.","journal-title":"Arch. Math."},{"issue":"3","key":"BF03321840_CR13","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1007\/s00006-010-0262-4","volume":"21","author":"R Delanghe","year":"2011","unstructured":"R. Delanghe, R. L\u00e1vi\u010dka and V. Soucek, On polynomial solutions of generalized Moisil-Th\u00e9odoresco systems and Hodge systems, Adv. Appl. Clifford Alg. 21 no.3 (2011), 521\u2013530.","journal-title":"Adv. Appl. Clifford Alg."},{"key":"BF03321840_CR14","unstructured":"D. Pe\u00f1a Pe\u00f1a, On a sequence of monogenic polynomials satisfying the Appell condition whose first term is a non-constant function, arXiv:1102.1833 [math.CV] (2011), submitted."},{"key":"BF03321840_CR15","unstructured":"\u2014, Shifted Appell sequences in Clifford analysis, arXiv:1102.4373 [math.CV] (2011), submitted."},{"key":"BF03321840_CR16","unstructured":"M. Falc\u00e3o, J. Cruz and H. Malonek, Remarks on the generation of monogenic functions, in: K. G\u00fcrlebeck and C. K\u00f6nke (eds.) Proceedings 17th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering, Weimar, 2006."},{"key":"BF03321840_CR17","doi-asserted-by":"crossref","unstructured":"M. Falc\u00e3o and H. Malonek, Generalized exponentials through Appell sets in \u211dn+1 and Bessel functions, AIP-Proceedings (2007), 738\u2013741.","DOI":"10.1063\/1.2790257"},{"key":"BF03321840_CR18","doi-asserted-by":"crossref","unstructured":"\u2014, Special monogenic polynomials \u2014 properties and applications, AlP-Proceedings (2007), 764\u2013767.","DOI":"10.1063\/1.2790265"},{"key":"BF03321840_CR19","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/BF01202702","volume":"4","author":"R Fueter","year":"1932","unstructured":"R. Fueter, Analytische Funktionen einer Quaternionenvariablen, Comment. Math. Helv. 4 (1932), 9\u201320.","journal-title":"Comment. Math. Helv."},{"key":"BF03321840_CR20","volume-title":"Functions of a Hypercomplex Variable","author":"R Fueter","year":"1949","unstructured":"R. Fueter, Functions of a Hypercomplex Variable, lecture notes written and supplemented by E. Bareiss, Math. Inst. Univ. Z\u00fcrich, Fall Semester, 1949."},{"key":"BF03321840_CR21","volume-title":"Quaternionic and Clifford Calculus for Engineers and Physicists","author":"K G\u00fcrlebeck","year":"1997","unstructured":"K. G\u00fcrlebeck and W. Spr\u00f6ssig, Quaternionic and Clifford Calculus for Engineers and Physicists, John Wiley and Sons, Chichester, 1997."},{"issue":"4","key":"BF03321840_CR22","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/S0378-4754(97)00066-9","volume":"44","author":"K G\u00fcrlebeck","year":"1997","unstructured":"K. G\u00fcrlebeck and W. Spr\u00f6ssig, On the treatment of fluid problems by methods of Clifford analysis, Math. Comput. Simulation 44 no.4 (1997), 401\u2013413.","journal-title":"Math. Comput. Simulation"},{"issue":"3","key":"BF03321840_CR23","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1080\/17476939908815192","volume":"39","author":"K G\u00fcrlebeck","year":"1999","unstructured":"K. G\u00fcrlebeck and H. Malonek, A hypercomplex derivative of monogenic functions in \u211dn+1 and its applications, Complex Variables 39 no.3 (1999), 199\u2013228.","journal-title":"Complex Variables"},{"key":"BF03321840_CR24","volume-title":"Holomorphic Functions in the Plane and n-Dimensional Space","author":"K G\u00fcrlebeck","year":"2008","unstructured":"K. G\u00fcrlebeck, K. Habetha and W. Spr\u00f6\u00dfig, Holomorphic Functions in the Plane and n-Dimensional Space, Birkh\u00e4user Verlag, Basel\/Boston\/Berlin, 2008."},{"issue":"1","key":"BF03321840_CR25","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s00006-008-0126-3","volume":"19","author":"N G\u00fcrlebeck","year":"2009","unstructured":"N. G\u00fcrlebeck, On Appell Sets and the Fueter-Sce Mapping, Adv. Appl. Clifford Algebras 19 no.1 (2009), 51\u201361.","journal-title":"Adv. Appl. Clifford Algebras"},{"key":"BF03321840_CR26","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1063\/1.3636724","volume":"1389","author":"R L\u00e1vicka","year":"2011","unstructured":"R. L\u00e1vicka, Generalized Appell property for the Riesz system in dimension 3, AIP Conference Proceedings 1389 (2011), 291\u2013294.","journal-title":"AIP Conference Proceedings"},{"key":"BF03321840_CR27","unstructured":"\u2014, Complete orthogonal Appell systems for spherical monogenics, arXiv:1106.2970v1 [math.CV] (2011), submitted."},{"issue":"2","key":"BF03321840_CR28","first-page":"213","volume":"27","author":"E Lindel\u00f6f","year":"1903","unstructured":"E. Lindel\u00f6f, Sur la d\u00e9termination de la croissance des fonctions enti`eres de\u00e9finies par un d\u00e9veloppement de Taylor, Darb. Bull. 27 no.2 (1903), 213\u2013226.","journal-title":"Darb. Bull."},{"issue":"3","key":"BF03321840_CR29","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1080\/17476939008814449","volume":"15","author":"H Malonek","year":"1990","unstructured":"H. Malonek, Power series representation for monogenic functions in \u211dm+1 based on a permutational product, Complex Var. 15 no.3 (1990), 181\u2013191.","journal-title":"Complex Var."},{"issue":"12","key":"BF03321840_CR30","doi-asserted-by":"crossref","first-page":"1472","DOI":"10.1002\/mma.1457","volume":"34","author":"J Morais","year":"2011","unstructured":"J. Morais and H.T. Le, Orthogonal Appell Systems of Monogenic Functions in the Cylinder, Math. Methods Appl. Sci. 34 no.12 (2011), 1472\u20131486.","journal-title":"Math. Methods Appl. Sci."},{"key":"BF03321840_CR31","first-page":"1651","volume":"5","author":"V Ozegov","year":"1964","unstructured":"V. Ozegov, Some extremal properties of generalized Appell polynomials, Soviet Math. 5 (1964), 1651\u20131653.","journal-title":"Soviet Math."},{"key":"BF03321840_CR32","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/BF01444962","volume":"58","author":"A Pringsheim","year":"1904","unstructured":"A. Pringsheim, Elementare Theorie der ganzen transzendenten Funktionen von endlicher Ordnung, Math. Ann. 58 (1904), 257\u2013342.","journal-title":"Math. Ann."},{"key":"BF03321840_CR33","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1215\/S0012-7094-39-00549-1","volume":"5","author":"I Sheffer","year":"1939","unstructured":"I. Sheffer, Some properties of polynomial sets of type zero, Duke Math. J. 5 (1939), 590\u2013622.","journal-title":"Duke Math. J."},{"issue":"12","key":"BF03321840_CR34","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1090\/S0002-9904-1941-07584-1","volume":"47","author":"I Sheffer","year":"1941","unstructured":"I. Sheffer, Some applications of certain polynomial classes, Bull. Amer. Math. Soc. 47 no.12 (1941), 885\u2013898.","journal-title":"Bull. Amer. Math. Soc."},{"issue":"10","key":"BF03321840_CR35","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1090\/S0002-9904-1945-08437-7","volume":"51","author":"I Sheffer","year":"1945","unstructured":"I. Sheffer, Note on Appell polynomials, Bull. Amer. Math. Soc. 51 no.10 (1945), 739\u2013744.","journal-title":"Bull. Amer. Math. Soc."},{"key":"BF03321840_CR36","doi-asserted-by":"crossref","first-page":"191","DOI":"10.2307\/2305676","volume":"52","author":"C Thorne","year":"1945","unstructured":"C. Thorne, A property of Appell sets, Amer. Math. Monthly 52 (1945), 191\u2013193.","journal-title":"Amer. Math. Monthly"},{"key":"BF03321840_CR37","volume-title":"Lectures on the General Theory of Integral Functions","author":"G Valiron","year":"1949","unstructured":"G. Valiron, Lectures on the General Theory of Integral Functions, Chelsea, New York, 1949."},{"key":"BF03321840_CR38","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/BF02401837","volume":"37","author":"A Wiman","year":"1914","unstructured":"A. Wiman, \u00dcber den Zusammenhang zwischen dem Maximalbetrage einer analytischen Funktion und dem gr\u00f6\u00dften Gliede der zugeh\u00f6rigen Taylorschen Reihe, Acta Math. 37 (1914), 305\u2013326.","journal-title":"Acta Math."},{"key":"BF03321840_CR39","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1090\/S0002-9904-1938-06896-6","volume":"44","author":"M Webster","year":"1938","unstructured":"M. Webster, Orthogonal polynomials with orthogonal derivatives, Bull. Amer. Math. Soc. 44 (1938), 880\u2013888.","journal-title":"Bull. Amer. Math. Soc."},{"key":"BF03321840_CR40","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1112\/jlms\/s1-10.1.108","volume":"10","author":"J Whittaker","year":"1935","unstructured":"J. Whittaker, The uniqueness of expansions in polynomials, J. London Math. Soc. 10 (1935), 108\u2013111.","journal-title":"J. London Math. Soc."},{"key":"BF03321840_CR41","volume-title":"Collection de monographies sur la theorie des fonctions","author":"J Whittaker","year":"1949","unstructured":"J. Whittaker, Sur les s\u00e9ries de base de polyn\u00f4mes quelconques, Avec la col laboration de C. Gattegno, Collection de monographies sur la theorie des fonctions, Paris, Gauthier-Villars. VI., 1949."}],"container-title":["Computational Methods and Function Theory"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF03321840.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF03321840\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF03321840","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T02:58:16Z","timestamp":1745981896000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF03321840"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,21]]},"references-count":41,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["BF03321840"],"URL":"https:\/\/doi.org\/10.1007\/bf03321840","relation":{},"ISSN":["1617-9447","2195-3724"],"issn-type":[{"value":"1617-9447","type":"print"},{"value":"2195-3724","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8,21]]}}}