লক্ষ্য করুন: এই এন্ট্রির অনুবাদ বর্তমানে মান পর্যালোচনার অধীনে রয়েছে, তাই কিছু বিষয়বস্তু সাময়িকভাবে শুধুমাত্র ইংরেজিতে প্রদর্শিত হচ্ছে।
এই এন্ট্রিটি এখনও আপনার ভাষায় অনুবাদ করা হয়নি, তাই নিচে মূল লেখাটি দেখানো হচ্ছে।
holomorphic
This term is a specialized technical descriptor used exclusively within complex analysis. It describes a function that is differentiable in a complex sense, which is a much more restrictive condition than real-differentiability. A function that is holomorphic on an open set is automatically analytic, meaning it can be represented by a convergent power series.
In mathematical discourse, the term is often used interchangeably with analytic when referring to functions of a complex variable. It carries a connotation of smoothness and rigidity, as the behavior of a holomorphic function on a small region determines its behavior everywhere else in its domain.
Meanings
Examples
A holomorphic function is complex differentiable at every point in its domain.
Is this mapping holomorphic on the entire unit disk?
I need to check if the function satisfies the Cauchy Riemann equations to prove it is holomorphic.
The professor explained that every holomorphic function is also infinitely differentiable.
Wait, if the function is holomorphic, then it must be analytic as well.
The researcher focused on the properties of holomorphic bundles over complex manifolds.
We are looking for a holomorphic extension of this function to a larger domain.
The integral of a holomorphic function around a closed contour is zero.