| 释义 |
branch (holomorphic branch) Given a multifunction f on an open subset U of ℂ, a holomorphic branch of f is a holomorphic function on U which selects from the possible choices of f(z) for each z ∈ U. Essentially, the branch is a holomorphic choice of principal values for f. For example, every z ∈ ℂ which is not a positive real can be written uniquely as z = reiθ on a cut plane where r>0 and 0 < θ < 2π. A holomorphic branch for the complex logarithm on this cut plane is then logr + iθ. Note that 0 is a branch point and that there is a discontinuity across the positive real axis of 2πi.
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