Complex Numbers in n Dimensions

ISBN: 9780444511232 出版年：2002 页码：286 Olariu, S North Holland_RM

1 Hyperbolic Complex Numbers in Two Dimensions 1.1 Operations with hyperbolic twocomplex numbers. 1.2 Geometric representation of hyperbolic twocomplex numbers. 1.3 Exponential and trigonometric forms of a twocomplex number. 1.4 Elementary functions of a twocomplex variable. 1.5 Twocomplex power series. 1.6 Analytic functions of twocomplex variables. 1.7 Integrals of twocomplex functions. 1.8 Factorization of twocomplex polynomials. 1.9 Representation of hyperbolic twocomplex numbers by irreducible matrices. 2 Complex Numbers in Three Dimensions 2.1 Operations with tricomplex numbers. 2.2 Geometric representation of tricomplex numbers. 2.3 The tricomplex cosexponential functions. 2.4 Exponential and trigonometric forms of tricomplex numbers. 2.5 Elementary functions of a tricomplex variable. 2.6 Tricomplex power series. 2.7 Analytic functions of tricomplex variables. 2.8 Integrals of tricomplex functions. 2.9 Factorization of tricomplex polynomials. 2.10 Representation of tricomplex numbers by irreducible matrices. 3 Commutative Complex Numbers in 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 fourcomplex numbers. 3.1.4 Elementary functions of a circular fourcomplex variable. 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. 3.1.9 Representation of circular fourcomplex numbers by irreducible matrices. 3.2 Hyperbolic complex numbers in four dimensions. 3.2.1 Operations with hyperbolic fourcomplex numbers. 3.2.2 Geometric representation of hyperbolic fourcomplex numbers. 3.2.3 Exponential form of a hyperbolic fourcomplex number. 3.2.4 Elementary functions of a hyperbolic fourcomplex variable. 3.2.5 Power series of hyperbolic fourcomplex variables. 3.2.6 Analytic functions of hyperbolic fourcomplex variables. 3.2.7 Integrals of functions of hyperbolic fourcomplex variables. 3.2.8 Factorization of hyperbolic fourcomplex polynomials. 3.2.9 Representation of hyperbolic fourcomplex numbers by irreducible matrices. 3.3 Planar complex numbers in four dimensions. 3.3.1 Operations with planar fourcomplex numbers. 3.3.2 Geometric representation of planar fourcomplex numbers. 3.3.3 The planar fourdimensional cosexponential functions. 3.3.4 The exponential and trigonometric forms of planar fourcomplex numbers. 3.3.5 Elementary functions of planar fourcomplex variables. 3.3.6 Power series of planar fourcomplex variables. 3.3.7 Analytic functions of planar fourcomplex variables. 3.3.8 Integrals of functions of planar fourcomplex variables. 3.3.9 Factorization of planar fourcomplex polynomials. 3.3.10 Representation of planar fourcomplex numbers by irreducible matrices. 3.4 Polar complex numbers in four dimensions. 3.4.1 Operations with polar fourcomplex numbers. 3.4.2 Geometric representation of polar fourcomplex numbers. 3.4.3 The polar fourdimensional cosexponential functions. 3.4.4 The exponential and trigonometric forms of a polar fourcomplex number. 3.4.5 Elementary functions of polar fourcomplex variables. 3.4.6 Power series of polar fourcomplex variables. 3.4.7 Analytic functions of polar fourcomplex variables. 3.4.8 Integrals of functions of polar fourcomplex variables. 3.4.9 Factorization of polar fourcomplex polynomials. 3.4.10 Representation of polar fourcomplex numbers by irreducible matrices. 4 Complex Numbers in 5 Dimensions 4.1 Operations with polar complex numbers in 5 dimensions. 4.2 Geometric representation of polar complex numbers in 5 dimensions. 4.3 The polar 5-dimensional cosexponential functions. 4.4 Exponential and trigonometric forms of polar 5-complex numbers. 4.5 Elementary functions of a polar 5-complex variable. 4.6 Power series of 5-complex numbers. 4.7 Analytic functions of a polar 5-complex variable. 4.8 Integrals of polar 5-complex functions. 4.9 Factorization of polar 5-complex polynomials. 4.10 Representation of polar 5-complex numbers by irreducible matrices 5 Complex Numbers in 6 Dimensions 5.1 Polar complex numbers in 6 dimensions. 5.1.1 Operations with polar complex numbers in 6 dimensions. 5.1.2 Geometric representation of polar complex numbers in 6 dimensions. 5.1.3 The polar 6-dimensional cosexponential functions. 5.1.4 Exponential and trigonometric forms of polar 6-complex numbers. 5.1.5 Elementary functions of a polar 6-complex variable. 5.1.6 Power series of polar 6-complex numbers. 5.1.7 Analytic functions of a polar 6-complex variable. 5.1.8 Integrals of polar 6-complex functions. 5.1.9 Factorization of polar 6-complex polynomials. 5.1.10 Representation of polar 6-complex numbers by irreducible matrices. 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 Analytic functions of a planar 6-complex variable. 5.2.8 Integrals of planar 6-complex functions. 5.2.9 Factorization of planar 6-complex polynomials. 5.2.10 Representation of planar 6-complex numbers by irreducible matrices. 6 Commutative Complex Numbers in n Dimensions 6.1 Polar complex numbers in n dimensions. 6.1.1 Operations with polar n-complex numbers. 6.1.2 Geometric representation of polar n-complex numbers. 6.1.3 The polar n-dimensional cosexponential functions. 6.1.4 Exponential and trigonometric forms of polar n-complex numbers. 6.1.5 Elementary functions of a polar n-complex variable. 6.1.6 Power series of polar n-complex numbers. 6.1.7 Analytic functions of polar n-complex variables. 6.1.8 Integrals of polar n-complex functions. 6.1.9 Factorization of polar n-complex polynomials. 6.1.10 Representation of polar n-complex numbers by irreducible matrices. 6.2 Planar complex numbers in even n dimensions. 6.2.1 Operations with planar n-complex numbers. 6.2.2 Geometric representation of planar n-complex numbers. 6.2.3 The planar n-dimensional cosexponential functions. 6.2.4 Exponential and trigonometric forms of planar n-complex numbers. 6.2.5 Elementary functions of a planar n-complex variable. 6.2.6 Power series of planar n-complex numbers. 6.2.7 Analytic functions of planar n-complex variables. 6.2.8 Integrals of planar n-complex functions. 6.2.9 Factorization of planar n-complex polynomials. 6.2.10 Representation of planar n-complex numbers by irreducible matrices. Bibliography. Index