Named special functions.

Entity["MathematicalFunction",name] or

represents an entity of type "MathematicalFunction".


gives the value of a specified property.


gives the value of a list of properties.


gives the value of a specified property modified by qualifier rules quali->vali.


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

Sample Entities

Sample Entity Classes


  • AdditionFormulasaddition formulas
    AlternativeRepresentationsalternative representations
    ArgumentPatternargument pattern
    ArgumentSimplificationsargument simplifications
    AsymptoticExpansionsasymptotic expansions
    ComplexCharacteristicscomplex characteristics
    ContinuedFractionRepresentationscontinued fraction representations
    DifferenceEquationsdifference equations
    DifferentialEquationsdifferential equations
    EntityClassesentity classes
    FourierTransformsFourier transforms
    FractionalDerivativesfractional derivatives
    FunctionalEquationsfunctional equations
    GeneratingFunctionsgenerating functions
    HalfArgumentFormulashalfargument formulas
    HankelTransformsHankel transforms
    HypergeometricRepresentationshypergeometric representations
    IntegralRepresentationsintegral representations
    InverseFourierTransformsinverse Fourier transforms
    InverseFunctionRelationsinverse function relations
    LaplaceTransformsLaplace transforms
    LimitRepresentationslimit representations
    LowOrderDerivativesloworder derivatives
    MellinTransformsMellin transforms
    MultipliedArgumentFormulasmultipliedargument formulas
    NamedIdentitiesnamed identities
    ParticularValuesparticular values
    ProductOfFunctionsFormulasproductoffunctions formulas
    ProductRepresentationsproduct representations
    ReflectionSymmetriesreflection symmetries
    RelatedFunctionRepresentationsrelated function representations
    RelatedFunctionsrelated functions
    RelatedIdentitiesrelated identities
    RelatedInequalitiesrelated inequalities
    ResidueRepresentationsresidue representations
    SampleDefiniteIntegralssample definite integrals
    SampleFiniteProductssample finite products
    SampleFiniteSumssample finite sums
    SampleIndefiniteIntegralssample indefinite integrals
    SampleInfiniteProductssample infinite products
    SampleInfiniteSumssample infinite sums
    SampleIntegralssample integrals
    SeriesRepresentationsseries representations
    SummedTaylorSeriesLimitssummed Taylor series limits
    SumOfFunctionsFormulassumoffunctions formulas
    SymbolicDerivativessymbolic derivatives
    TraditionalFormBoxestraditional form boxes
    WolframFunctionsSiteLinkWolfram Functions Site link


  • "MathematicalFunction" entities represent special mathematical functions appearing often enough in the literature of mathematics, physics, engineering or another application to have an accepted name and/or notation.
  • "MathematicalFunction" entity classes include sets of functions.
  • Some properties are available for the "MathematicalFunction" entity type as a whole and can be given using the form EntityValue["MathematicalFunction",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["MathematicalFunction",property,annotation]:
  • "Source"source information for the property
    "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
  • 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.


Basic Examples  (4)

Use MathematicalFunctionData to find the Entity corresponding to a given function:

Find a property value for an entity:

Retrieve a dataset of all available properties for an entity:

Find mathematical functions related to the Gudermannian function:

Introduced in 2019