Olariu, Silviu. 　著

内容

目次

1 Hyperbolic Complex Numbers in Two Dimensions 1.1 Operationswith hyperbolic twocomplex numbers. 1.2 Geometric representation ofhyperbolic twocomplex numbers. 1.3 Exponential and trigonometric formsof a twocomplex number. 1.4 Elementary functions of a twocomplexvariable. 1.5 Twocomplex power series. 1.6 Analytic functionsof twocomplex variables. 1.7 Integrals of twocomplex functions.1.8 Factorization of twocomplex polynomials. 1.9 Representation ofhyperbolic twocomplex numbers by irreducible matrices. 2 Complex Numbersin Three Dimensions 2.1 Operations with tricomplex numbers. 2.2Geometric representation of tricomplex numbers. 2.3 The tricomplexcosexponential functions. 2.4 Exponential and trigonometric forms oftricomplex numbers. 2.5 Elementary functions of a tricomplex variable.2.6 Tricomplex power series. 2.7 Analytic functions of tricomplexvariables. 2.8 Integrals of tricomplex functions. 2.9Factorization of tricomplex polynomials. 2.10 Representation oftricomplex numbers by irreducible matrices. 3 Commutative Complex Numbersin Four Dimensions. 3.1 Circular complex numbers in four dimensions.3.1.1 Operations with circular fourcomplex numbers.3.1.2 Geometric representation of circular fourcomplex numbers.3.1.3 The exponential and trigonometric forms of circular fourcomplexnumbers. 3.1.4 Elementary functions of a circular fourcomplexvariable. 3.1.5 Power series of circular fourcomplex variables.3.1.6 Analytic functions of circular fourcomplex variables.3.1.7 Integrals of functions of circular fourcomplex variables.3.1.8 Factorization of circular fourcomplex polynomials. 3.1.9Representation of circular fourcomplex numbers by irreducible matrices.3.2 Hyperbolic complex numbers in four dimensions. 3.2.1Operations with hyperbolic fourcomplex numbers. 3.2.2 Geometricrepresentation of hyperbolic fourcomplex numbers. 3.2.3Exponential form of a hyperbolic fourcomplex number. 3.2.4Elementary functions of a hyperbolic fourcomplex variable. 3.2.5Power series of hyperbolic fourcomplex variables. 3.2.6 Analyticfunctions of hyperbolic fourcomplex variables. 3.2.7 Integrals offunctions of hyperbolic fourcomplex variables. 3.2.8Factorization of hyperbolic fourcomplex polynomials. 3.2.9Representation of hyperbolic fourcomplex numbers by irreducible matrices.3.3 Planar complex numbers in four dimensions. 3.3.1Operations with planar fourcomplex numbers. 3.3.2 Geometricrepresentation of planar fourcomplex numbers. 3.3.3 The planarfourdimensional cosexponential functions. 3.3.4 The exponentialand trigonometric forms of planar fourcomplex numbers. 3.3.5Elementary functions of planar fourcomplex variables. 3.3.6 Powerseries of planar fourcomplex variables. 3.3.7 Analytic functionsof planar fourcomplex variables. 3.3.8 Integrals of functions ofplanar fourcomplex variables. 3.3.9 Factorization of planarfourcomplex polynomials. 3.3.10 Representation of planarfourcomplex numbers by irreducible matrices. 3.4 Polar complexnumbers in four dimensions. 3.4.1 Operations with polarfourcomplex numbers. 3.4.2 Geometric representation of polarfourcomplex numbers. 3.4.3 The polar fourdimensionalcosexponential functions. 3.4.4 The exponential and trigonometricforms of a polar fourcomplex number. 3.4.5 Elementary functionsof polar fourcomplex variables. 3.4.6 Power series of polarfourcomplex variables. 3.4.7 Analytic functions of polarfourcomplex variables. 3.4.8 Integrals of functions of polarfourcomplex variables. 3.4.9 Factorization of polar fourcomplexpolynomials. 3.4.10 Representation of polar fourcomplex numbers byirreducible matrices. 4 Complex Numbers in 5 Dimensions 4.1Operations with polar complex numbers in 5 dimensions. 4.2 Geometricrepresentation of polar complex numbers in 5 dimensions. 4.3 The polar5-dimensional cosexponential functions. 4.4 Exponential andtrigonometric forms of polar 5-complex numbers. 4.5 Elementaryfunctions of a polar 5-complex variable. 4.6 Power series of 5-complexnumbers. 4.7 Analytic functions of a polar 5-complex variable.4.8 Integrals of polar 5-complex functions. 4.9 Factorization ofpolar 5-complex polynomials. 4.10 Representation of polar 5-complexnumbers by irreducible matrices 5 Complex Numbers in 6 Dimensions5.1 Polar complex numbers in 6 dimensions. 5.1.1 Operationswith polar complex numbers in 6 dimensions. 5.1.2 Geometricrepresentation of polar complex numbers in 6 dimensions. 5.1.3The polar 6-dimensional cosexponential functions. 5.1.4Exponential and trigonometric forms of polar 6-complex numbers.5.1.5 Elementary functions of a polar 6-complex variable. 5.1.6Power series of polar 6-complex numbers. 5.1.7 Analytic functionsof a polar 6-complex variable. 5.1.8 Integrals of polar 6-complexfunctions. 5.1.9 Factorization of polar 6-complex polynomials.5.1.10 Representation of polar 6-complex numbers by irreduciblematrices. 5.2 Planar complex numbers in 6 dimensions.5.2.1 Operations with planar complex numbers in 6 dimensions.5.2.2 Geometric representation of planar complex numbers in 6 dimensions.5.2.3 The planar 6-dimensional cosexponential functions.5.2.4 Exponential and trigonometric forms of planar 6-complex numbers.5.2.5 Elementary functions of a planar 6-complex variable.5.2.6 Power series of planar 6-complex numbers. 5.2.7 Analyticfunctions of a planar 6-complex variable. 5.2.8 Integrals ofplanar 6-complex functions. 5.2.9 Factorization of planar6-complex polynomials. 5.2.10 Representation of planar 6-complexnumbers by irreducible matrices. 6 Commutative Complex Numbers in nDimensions 6.1 Polar complex numbers in n dimensions.6.1.1 Operations with polar n-complex numbers. 6.1.2 Geometricrepresentation of polar n-complex numbers. 6.1.3 The polarn-dimensional cosexponential functions. 6.1.4 Exponential andtrigonometric forms of polar n-complex numbers. 6.1.5 Elementaryfunctions of a polar n-complex variable. 6.1.6 Power series ofpolar n-complex numbers. 6.1.7 Analytic functions of polarn-complex variables. 6.1.8 Integrals of polar n-complexfunctions. 6.1.9 Factorization of polar n-complex polynomials.6.1.10 Representation of polar n-complex numbers by irreduciblematrices. 6.2 Planar complex numbers in even n dimensions.6.2.1 Operations with planar n-complex numbers. 6.2.2 Geometricrepresentation of planar n-complex numbers. 6.2.3 The planarn-dimensional cosexponential functions. 6.2.4 Exponential andtrigonometric forms of planar n-complex numbers. 6.2.5 Elementaryfunctions of a planar n-complex variable. 6.2.6 Power series ofplanar n-complex numbers. 6.2.7 Analytic functions of planarn-complex variables. 6.2.8 Integrals of planar n-complexfunctions. 6.2.9 Factorization of planar n-complex polynomials.6.2.10 Representation of planar n-complex numbers by irreduciblematrices. Bibliography. Index