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Escola Superior de Tecnologia e Gestão (ESTG) >
Artigos em Revista Internacional (ESTG) >
Utilize este identificador para referenciar este registo:
http://hdl.handle.net/10314/5249
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| Título: | A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis |
| Autores: | Cação, Isabel
Falcão, M. Irene
Malonek, Helmuth R.
Tomaz, Graça |
| Palavras Chave: | Clifford algebra
hypercomplex analysis
Sturm-Liouville equation
Vietoris' numbers |
| Data: | 9-Aug-2021 |
| Editora: | John Wiley and Sons Ltd |
| Resumo: | The paper studies discrete structural properties of polynomials that play an
important role in the theory of spherical harmonics in any dimension. These
polynomials have their origin in the research on problems of harmonic analysis
by means of generalized holomorphic (monogenic) functions of hypercomplex
analysis. The Sturm-Liouville equation that occurs in this context supplements
the knowledge about generalized Vietoris number sequences Vn, first encountered
as a special sequence (corresponding to n = 2) by Vietoris in connection
with positivity of trigonometric sums. Using methods of the calculus of holonomic
differential equations, we obtain a general recurrence relation for Vn,
and we derive an exponential generating function of Vn expressed by Kummer's
confluent hypergeometric function. |
| URI: | http://hdl.handle.net/10314/5249 |
| ISSN: | 01704214, 10991476 |
| Aparece nas Colecções: | Artigos em Revista Internacional (ESTG)
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Ficheiros deste Registo:
| Ficheiro |
Descrição |
Tamanho | Formato |
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| PDFsam_repSturm-liouville.pdf | | 59Kb | Adobe PDF | Ver/Abrir | |
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