41. Several complex variables is the study of such holomorphic functions in " n " variables. 42. As a consequence of the Cauchy Riemann equations, a real-valued holomorphic function must be constant. 43. It is a quick check that the Cauchy integral theorem also holds for vector-valued holomorphic functions . 44. Then I map this with the holomorphic function , it must be an open set and it contains c. 45. In this context the extension of holomorphic functions of a complex variable is developed as the holomorphic functional calculus. 46. :: Often complex dynamics refers to dynamical systems that arise by iterating holomorphic functions in a complex domain. 47. A consequence of this restriction is that the Laplace transform of a function is a holomorphic function of the variable. 48. Unlike functions of a real variable, holomorphic functions are sufficiently rigid that their isolated singularities can be completely classified. 49. Complex manifolds are introduced in an analogous way by requiring that the transition functions of an atlas are holomorphic functions . 50. More can be done : one can consider polynomials of Grassman numbers, leading to the idea of holomorphic functions .
