Exponential forms and path integrals for complex numbers in n dimensions
Two distinct systems of commutative complex numbers in n dimensions are described, of polar and planar types. Exponential forms of n-complex numbers are given in each case, which depend on geometric variables. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and t...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120102004X |
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| Summary: | Two distinct systems of commutative complex numbers in n dimensions are described, of polar and planar types. Exponential
forms of n-complex numbers are given in each case, which depend on
geometric variables. Azimuthal angles, which are cyclic variables,
appear in these forms at the exponent, and this leads to the
concept of residue for path integrals of n-complex functions. The
exponential function of an n-complex number is expanded in terms
of functions called in this paper cosexponential functions, which
are generalizations to n dimensions of the circular and
hyperbolic sine and cosine functions. The factorization of
n-complex polynomials is discussed. |
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| ISSN: | 0161-1712 1687-0425 |