isIntegralFormOf
P28827
predicate
Indicates that one entity is the integral (indefinite integral or antiderivative) form corresponding to another entity, typically a derivative or differential expression.
All labels observed (4)
| Label | Occurrences |
|---|---|
| integralRepresentation | 3 |
| definedByIntegral | 2 |
| isIntegralFormOf canonical | 1 |
| standardFormIntegral | 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: isIntegralFormOf
Generated description
Indicates that one entity is the integral (indefinite integral or antiderivative) form corresponding to another entity, typically a derivative or differential expression.
Sample triples (7)
| Subject | Object |
|---|---|
| Gauss's law for magnetism | ∇ · B = 0 ⓘ |
| Ampère–Maxwell law | ∮_C B · dl = μ₀I_enclosed + μ₀ε₀ dΦ_E/dt via predicate surface "standardFormIntegral" ⓘ |
| Heaviside step function | H(x)=∫_{-∞}^x δ(t) dt (in distribution sense) via predicate surface "integralRepresentation" ⓘ |
|
Fresnel integrals
surface form:
Fresnel sine integral
|
S(x) = ∫₀ˣ sin(π t² / 2) dt via predicate surface "definedByIntegral" ⓘ |
|
Fresnel integrals
surface form:
Fresnel cosine integral
|
C(x) = ∫₀ˣ cos(π t² / 2) dt via predicate surface "definedByIntegral" ⓘ |
|
Euler–Mascheroni constant γ
surface form:
Euler–Mascheroni constant
|
γ = ∫_0^∞ (e^{−x}/x − e^{−x}/(1 − e^{−x})) dx via predicate surface "integralRepresentation" ⓘ |
|
Euler–Mascheroni constant γ
surface form:
Euler–Mascheroni constant
|
γ = ∫_0^1 (1 − H_x) dx where H_x is analytically continued via predicate surface "integralRepresentation" ⓘ |