Clifford analysis between continuous and discrete

• Main Author: Malonek, H. R.
• Publication Date: 2008
• Other Authors: Falcão, M. I.
• Language: eng
• Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Download full: http://hdl.handle.net/1822/17076
• topic: Homogeneous monogenic polynomials; Quaternions; Appell sets; Science & Technology

Some decades ago D. Knuth et al. have coined concrete mathematics as the blending of CONtinuous and disCRETE math, taking into account that problems of standard discrete mathematics can often be solved by methods based on continuous mathematics together with a controlled manipulation of mathematical formulas. Of course, it was not a new idea, but due to the ongoing emergence of computer aided algebraic manipulation tools of that time it emphasized their use for elegant solutions of old problems or even the detection of new important relationships. Our aim is to show that the same philosophy can be successfully applied to Clifford Analysis by taking advantages of its inherent non-commutative algebra to obtain results or develop methods that are di erent from other ones. In particular, we determine new binomial sums by using a hypercomplex generating function for a special type of monogenic polynomials and develop an algorithm for the determination of their scalar and vector part which illustrates well the diifferences to the corresponding complex case.