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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832551508361609216 |
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| author | Silviu Olariu |
| author_facet | Silviu Olariu |
| author_sort | Silviu Olariu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-045a92e2ab734f81933deef0fdc24bf2 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-045a92e2ab734f81933deef0fdc24bf22025-02-03T06:01:12ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0125742945010.1155/S016117120102004XExponential forms and path integrals for complex numbers in n dimensionsSilviu Olariu0Institute of Physics and Nuclear Engineering, Tandem Laboratory, 76900 Magurele, P.O. Box MG-6, Bucharest, RomaniaTwo 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.http://dx.doi.org/10.1155/S016117120102004X |
| spellingShingle | Silviu Olariu Exponential forms and path integrals for complex numbers in n dimensions International Journal of Mathematics and Mathematical Sciences |
| title | Exponential forms and path integrals for complex
numbers in n dimensions |
| title_full | Exponential forms and path integrals for complex
numbers in n dimensions |
| title_fullStr | Exponential forms and path integrals for complex
numbers in n dimensions |
| title_full_unstemmed | Exponential forms and path integrals for complex
numbers in n dimensions |
| title_short | Exponential forms and path integrals for complex
numbers in n dimensions |
| title_sort | exponential forms and path integrals for complex numbers in n dimensions |
| url | http://dx.doi.org/10.1155/S016117120102004X |
| work_keys_str_mv | AT silviuolariu exponentialformsandpathintegralsforcomplexnumbersinndimensions |