valueAt
P43786
predicate
Indicates that one entity specifies the value or content associated with another entity at a particular point, position, or context.
All labels observed (11)
| Label | Occurrences |
|---|---|
| valueAt canonical | 44 |
| valueAtZero | 5 |
| valueAtOne | 4 |
| barValue | 1 |
| haveValueAtMinusOne | 1 |
| valueAtFive | 1 |
| valueAtFour | 1 |
| valueAtMinusOne | 1 |
| valueAtPrime | 1 |
| valueAtTwo | 1 |
| valueOnUnknot | 1 |
Sample triples (61)
| Subject | Object |
|---|---|
| Euler’s totient function φ(n) | φ(1) = 1 ⓘ |
| Euler’s totient function φ(n) | φ(2) = 1 ⓘ |
| Euler’s totient function φ(n) | φ(3) = 2 ⓘ |
| Euler’s totient function φ(n) | φ(4) = 2 ⓘ |
| Euler’s totient function φ(n) | φ(5) = 4 ⓘ |
| Euler’s totient function φ(n) | φ(6) = 2 ⓘ |
| Euler’s totient function φ(n) | φ(7) = 6 ⓘ |
| Euler’s totient function φ(n) | φ(8) = 4 ⓘ |
| Euler’s totient function φ(n) | φ(9) = 6 ⓘ |
| Euler’s totient function φ(n) | φ(10) = 4 ⓘ |
| Heaviside step function | H(0) is convention-dependent ⓘ |
| Gamma function | Γ(1)=1 ⓘ |
| Gamma function | Γ(1/2)=√π ⓘ |
| Gamma function | Γ(n)=(n-1)! for n∈ℕ ⓘ |
| Maya numerals | 5 via predicate surface "barValue" ⓘ |
| Jones polynomial | 1 via predicate surface "valueOnUnknot" ⓘ |
|
Lambert W function (later named in his honor)
surface form:
Lambert W function
|
W(0) = 0 ⓘ |
|
Lambert W function (later named in his honor)
surface form:
Lambert W function
|
W(-1/e) = -1 ⓘ |
|
Lambert W function (later named in his honor)
surface form:
Lambert W function
|
W(e) ≈ 1 ⓘ |
| Jordan’s totient functions | J_k(1) = 1 via predicate surface "valueAtOne" ⓘ |
| Jordan’s totient functions | J_k(p) = p^k - 1 via predicate surface "valueAtPrime" ⓘ |
| Ramanujan tau function | τ(1) = 1 ⓘ |
| Ramanujan tau function | τ(2) = -24 ⓘ |
| Ramanujan tau function | τ(3) = 252 ⓘ |
| Ramanujan tau function | τ(4) = -1472 ⓘ |
| Ramanujan tau function | τ(5) = 4830 ⓘ |
| Ramanujan tau function | τ(7) = -16744 ⓘ |
| Ramanujan tau function | τ(8) = 84480 ⓘ |
| Ramanujan tau function | τ(9) = -113643 ⓘ |
| Ramanujan tau function | τ(10) = -115920 ⓘ |
| Dirichlet eta function | η(0) = 1/2 ⓘ |
| Dirichlet eta function | η(1) = ln(2) ⓘ |
| Dirichlet eta function | η(2) = π^2 / 12 ⓘ |
| Dirichlet eta function | η(−1) = 1/4 ⓘ |
| Dirichlet eta function | η(−2n) = 0 for positive integer n ⓘ |
| Dirichlet kernel | D_n(0) = 2n+1 via predicate surface "valueAtZero" ⓘ |
| Catalan numbers | C_0 = 1 via predicate surface "valueAtZero" ⓘ |
| Catalan numbers | C_1 = 1 via predicate surface "valueAtOne" ⓘ |
| Catalan numbers | C_2 = 2 via predicate surface "valueAtTwo" ⓘ |
| Catalan numbers | C_4 = 14 via predicate surface "valueAtFour" ⓘ |
| Catalan numbers | C_5 = 42 via predicate surface "valueAtFive" ⓘ |
| Liouville function | λ(1) = 1 ⓘ |
| Liouville function | λ(p) = -1 for any prime p ⓘ |
| Liouville function | λ(p^k) = (-1)^k for any prime p and integer k ≥ 1 ⓘ |
| Legendre polynomials | P_n(-1) = (-1)^n via predicate surface "haveValueAtMinusOne" ⓘ |
| Chebyshev polynomials of the first kind | T_n(1) = 1 via predicate surface "valueAtOne" ⓘ |
| Chebyshev polynomials of the first kind | T_n(-1) = (-1)^n via predicate surface "valueAtMinusOne" ⓘ |
| Chebyshev polynomials of the first kind | T_{2k}(0) = (-1)^k via predicate surface "valueAtZero" ⓘ |
| Chebyshev polynomials of the first kind | T_{2k+1}(0) = 0 via predicate surface "valueAtZero" ⓘ |
| Gegenbauer polynomials | C_n^{(\lambda)}(1) = \binom{n+2\lambda-1}{n} ⓘ |