ContinuedFraction

Continued fraction identities.

Entity["ContinuedFraction",name] or

represents an entity of type "ContinuedFraction".

[prop]

gives the value of a specified property.

[{propi,}]

gives the value of a list of properties.

EntityClass["ContinuedFraction",{propispeci,}]

represents a class of entities with values of propi defined by speci.

Sample Entities

Sample Entity Classes

Properties

  • AssociatedPeopleassociated people
    Classesclasses
    Conditionscontinued fraction convergence conditions
    ContinuedFractioncontinued fraction
    ContinuedFractionIdentityidentity
    ContinuedFractionIdentityWithConditionsidentity with conditions
    ConvergencePointsconvergence points
    ConvergenceRegionPlotconvergence region plot
    ConvergentsCollapsedconvergents
    ConvergentsStackedstacked convergents
    EntityClassesentity classes
    EquivalentGenericCaseCFInDenominatorgeneric case in denominator
    EquivalentGenericCaseCFInNumeratorgeneric case in numerator
    EquivalentPartialDenominatorEqualToConstantpartial denominator equal to constant
    EquivalentPartialDenominatorEqualToOnepartial denominator equal to 1
    EquivalentPartialNumeratorEqualToConstantpartial numerator equal to constant
    EquivalentPartialNumeratorEqualToOnepartial numerator equal to 1
    EquivalentRemovingMinusFromPartialDenominatorremoving minus from partial denominator
    EquivalentToEvenContractioneven contraction
    EquivalentToOddContractionodd contraction
    FormattedReferencesformatted references
    Functionfunction
    Namename
    NamedMembersnamed members
    NthConvergentn th convergent
    Typestypes
    Variablesvariables

Details

  • "ContinuedFraction" entities include notable continued fraction identities for mathematical functions and constants.
  • "ContinuedFraction" entity classes include mathematical types of continued fraction identities such as "CFraction", "StieltjesFraction", and "JFraction", as well as groups of identities classified by the primary functions being represented, such as "Cos", "CosAll", and "CosCompound".
  • Some properties are available for the "ContinuedFraction" entity type as a whole and can be given using the form EntityValue["ContinuedFraction",property]. Such properties include:
  • "Properties"the list of available properties
    "PropertyCanonicalNames"the standard names of available properties
    "SampleEntities"a sample list of available entities (typically of length 10)
    "SampleEntityClasses"a sample list of available entity classes (typically of length 10)
    "EntityCount"number of entities available
    "Entities"the list of available entities
    "EntityCanonicalNames"the standard names of available entities
    "EntityClasses"the list of available entity classes
    "EntityClassCanonicalNames"the standard names of available entity classes
    "PropertyClasses"the list of available property classes
    "PropertyClassCanonicalNames"the standard names of available property classes
    "PropertyCount"number of properties available
  • The following annotations can be used in the third argument of EntityValue["ContinuedFraction",property,annotation]:
  • "Source"source information for the property
    "Date"the date associated with the entity-property value (if any)
    "EntityAssociation"an association of entities and entity-property values
    "PropertyAssociation"an association of properties and entity-property values
    "EntityPropertyAssociation"an association in which the specified entities are keys, and values are a nested association of properties and entity-property values
    "PropertyEntityAssociation"an association in which the specified properties are keys, and values are a nested association of entities and entity-property values
    "Dataset"a dataset in which the specified entities are keys, and values are an association of property names and entity-property values
  • The following annotations can be used in the second argument of EntityValue[property,annotation]:
  • "Qualifiers"the list of possible qualifiers for the property
    "QualifierValues"the list of possible values that can be given to each qualifier
    "DefaultQualifierValues"the list of default values for the property's qualifiers
    "Description"a brief textual description of the property
    "Definition"a detailed textual definition of the property
    "PhysicalQuantity"the physical quantity associated with the entity-property value
    "Unit"the unit associated with the entity-property value
  • A qualifier value of Automatic indicates that an applicable format of values can be used; e.g. for the "Date" qualifier, this includes a proper date or date span.

Examples

Basic Examples  (4)

Use for entity discovery:

In[1]:=
Click for copyable input
In[2]:=
Click for copyable input

Find a property value for an entity:

In[1]:=
Click for copyable input
Out[1]//TraditionalForm=

Retrieve a dataset of all available properties for an entity:

In[1]:=
Click for copyable input
Out[1]=

Return entities corresponding to continued fraction identities associated with Ramanujan:

In[1]:=
Click for copyable input
Out[1]=

Display the identities:

In[2]:=
Click for copyable input
Out[2]=

Extract and display the identities directly:

In[3]:=
Click for copyable input
Out[3]=