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