Gauss’s constant
E29371
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
Statements (36)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical constant
→
number-theoretic constant → |
| appearsIn |
arithmetic–geometric mean identities
→
theory of elliptic integrals → theory of theta functions → |
| approximateValue |
0.8346268
→
0.834626841674073186281429732799046808 → |
| catalogCode |
OEIS A064988
→
|
| context |
classical analysis
→
elliptic curves over the complex numbers → modular forms → |
| definedAs |
1/(2^{1/4}·K(1/√2))
→
2^{-1/4}·K(1/√2)^{-1} → |
| definedVia |
arithmetic–geometric mean
→
|
| field |
complex analysis
→
elliptic function theory → number theory → theory of the lemniscate → |
| hasType |
transcendental constant (conjectured)
→
|
| namedAfter |
Carl Friedrich Gauss
→
|
| namedInHonorOf |
Carl Friedrich Gauss
→
|
| occursIn |
special values of elliptic integrals
→
special values of modular functions → |
| property |
dimensionless quantity
→
positive real number → |
| relatedCurve |
Bernoulli lemniscate
→
|
| relatedFunction |
complete elliptic integral of the first kind
→
|
| relatedTo |
Gaussian arithmetic–geometric mean
→
arithmetic–geometric mean of 1 and √2 → elliptic modulus k = 1/√2 → lemniscatic constant → lemniscatic elliptic functions → singular modulus of order 4 → |
| symbol |
G
→
|
| usedIn |
evaluation of certain definite integrals
→
evaluation of periods of the lemniscate → |
Referenced by (1)
| Subject (surface form when different) | Predicate |
|---|---|
|
Carl Friedrich Gauss
→
|
hasConceptNamedAfter |