| __Holomorphic function - Biocrawler__ *(Site not responding. Last check: 2007-10-31)* |

| | Because **complex** differentiation is linear and obeys the product, quotient, and chain rules: the sums, products and compositions of holomorphic functions are holomorphic, and the quotient of two holomorphic functions is holomorphic wherever the denominator is non-zero. |

| | Cauchy's integral **formula** states that every holomorphic function is inside a disk completely determined by its values on the disk's boundary. |

| | A **complex** analytic function of several **complex** variables is defined to be analytic and holomorphic at a point if it is locally expandable (within a polydisk, a cartesian product of disks, centered at that point) as a convergent power series in the variables. |

| www.biocrawler.com /encyclopedia/Holomorphic (641 words) |