Monogenic pseudo-complex power functions and their applications

The use of a non‐commutative algebra in hypercomplex function theory requires a large variety of different representations of polynomials suitably adapted to the solution of different concrete problems. Naturally arises the question of their relationships and the advantages or disadvantages of diffe...

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Veröffentlicht in:Mathematical methods in the applied sciences Jg. 37; H. 12; S. 1723 - 1735
Hauptverfasser: Cruz, Carla, Irene Falcão, Maria, Malonek, Helmuth R.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Freiburg Blackwell Publishing Ltd 01.08.2014
Wiley Subscription Services, Inc
Schlagworte:
Binomial coefficients
Binomials
Byproducts
Combinatorial analysis
combinatorial identities
Functions (mathematics)
functions of hypercomplex variables
generalized Appell polynomials
Mathematical analysis
Polynomials
Representations
ISSN:0170-4214, 1099-1476
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Zusammenfassung:The use of a non‐commutative algebra in hypercomplex function theory requires a large variety of different representations of polynomials suitably adapted to the solution of different concrete problems. Naturally arises the question of their relationships and the advantages or disadvantages of different types of polynomials. In this sense, the present paper investigates the intrinsic relationship between two different types of monogenic Appell polynomials. Several authors payed attention to the construction of complete sets of monogenic Appell polynomials, orthogonal with respect to a certain inner product, and used them advantageously for the study of problems in 3D‐elasticity and other problems. Our goal is to show that, as consequence of the binomial nature of those generalized Appell polynomials, their inner structure is determined by interesting combinatorial relations in which the central binomial coefficients play a special role. As a byproduct of own interest, a Riordan–Sofo type binomial identity is also proved. Copyright © 2013 John Wiley & Sons, Ltd.
Bibliographie:istex:318556F3D631B7685B73BEE6BF6379479450235C
ark:/67375/WNG-RJ0TR929-Q
ArticleID:MMA2931
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.2931