generalizedForm
P27178
predicate
Indicates that one entity is a more abstract, generalized version or broader form of another entity.
All labels observed (4)
| Label | Occurrences |
|---|---|
| hasGeneralForm | 15 |
| generalizedForm canonical | 2 |
| generalFormulationInvolves | 1 |
| generalRelativisticForm | 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: generalizedForm
Generated description
Indicates that one entity is a more abstract, generalized version or broader form of another entity.
Sample triples (19)
| Subject | Object |
|---|---|
|
Gauss’s law
surface form:
Gauss's law
|
∮_S D · dA = Q_free_enclosed ⓘ |
| Fermat number | F_n = 2^{2^n} + 1 via predicate surface "hasGeneralForm" ⓘ |
| Cauchy–Euler equation | a x^2 y'' + b x y' + c y = 0 via predicate surface "hasGeneralForm" ⓘ |
| Lambert series | \sum_{n=1}^{\infty} a(n) \frac{q^n}{1-q^n} via predicate surface "hasGeneralForm" ⓘ |
| Dirichlet series | ∑_{n=1}^{∞} a_n n^{-s} via predicate surface "hasGeneralForm" ⓘ |
| Waring's problem | for every k ≥ 2 there exists g(k) such that every natural number is a sum of at most g(k) k-th powers via predicate surface "hasGeneralForm" ⓘ |
| Karplus equation | 3J = A cos²(θ) + B cos(θ) + C via predicate surface "hasGeneralForm" ⓘ |
| Bernstein polynomials | B_{n,k}(x) = C(n,k) x^k (1-x)^{n-k} via predicate surface "hasGeneralForm" ⓘ |
| Mittag-Leffler function | E_{α,β}(z) via predicate surface "hasGeneralForm" NERFINISHED ⓘ |
| dAlembert operator | \Box = g^{\mu\nu} \nabla_\mu \nabla_\nu via predicate surface "generalRelativisticForm" ⓘ |
| Leibniz rule | d^n(fg)/dx^n = Σ_{k=0}^n (n choose k) f^{(k)} g^{(n-k)} via predicate surface "hasGeneralForm" ⓘ |
| Rydberg formula | 1/λ = R (1/n1² − 1/n2²) via predicate surface "hasGeneralForm" ⓘ |
|
Slater-type orbital basis sets
surface form:
Slater-type orbital basis set
|
R_{n,l}(r) = N r^{n-1} e^{-\zeta r} via predicate surface "hasGeneralForm" ⓘ |
| Volume conjecture | colored Jones polynomial evaluated at roots of unity via predicate surface "generalFormulationInvolves" ⓘ |
| Hill equation | Y = [L]^n / (K_d + [L]^n) via predicate surface "hasGeneralForm" ⓘ |
| Sturm–Liouville problem | -(d/dx)[p(x) y'(x)] + q(x) y(x) = λ w(x) y(x) via predicate surface "hasGeneralForm" ⓘ |
| Polyakov action | S = −(T/2) ∫ d^2σ √−h h^{ab} ∂_a X^μ ∂_b X^ν G_{μν}(X) via predicate surface "hasGeneralForm" ⓘ |
|
The Matching Law
surface form:
Matching Law
|
log(B1/B2) = a·log(R1/R2) + log b ⓘ |
|
Möbius transformations
surface form:
Möbius transformation
|
f(z) = (az + b) / (cz + d) via predicate surface "hasGeneralForm" ⓘ |