isHolomorphicOn
P71176
predicate
Indicates that a complex-valued function is complex differentiable at every point of a specified domain, i.e., holomorphic throughout that region.
All labels observed (3)
| Label | Occurrences |
|---|---|
| isHolomorphicOn canonical | 2 |
| hasTypicalRegionOfAnalyticity | 1 |
| holomorphicOn | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: isHolomorphicOn
Generated description
Indicates that a complex-valued function is complex differentiable at every point of a specified domain, i.e., holomorphic throughout that region.
Sample triples (4)
| Subject | Object |
|---|---|
| Gamma function | ℂ minus non-positive integers ⓘ |
| Dirichlet series | half-plane Re(s) > σ_c via predicate surface "hasTypicalRegionOfAnalyticity" ⓘ |
| modular j-invariant | upper half-plane via predicate surface "holomorphicOn" ⓘ |
|
T:z ↦ z+1
surface form:
T : z ↦ z + 1
|
upper half-plane ℍ ⓘ |