Wolfram Language & System 10.3 (2015)|Legacy Documentation

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gives the value of the specified property for the mathematical function specified by entity.

gives the sub-property annotation corresponding to the given entity and property.    

gives the property value with the property qualifiers , , set to the given values.

gives the sub-property annotation corresponding to the given entity and property with the property qualifiers , , set to the given values.


  • MathematicalFunctionData can be used to access identities involving mathematical functions.
  • MathematicalFunctionData[] gives a list of all mathematical function entities.
  • MathematicalFunctionData["Properties"] gives a list of available properties.
  • MathematicalFunctionData["SampleEntities"] gives a list of sample entities.
  • The specified entity in MathematicalFunctionData can be an Entity, EntityClass, entity canonical name, or list thereof.
  • The specified property can be an EntityProperty, EntityPropertyClass, property canonical name, or list of properties.
  • MathematicalFunctionData entity-property values are generally lists of pure functions that can be applied to user-supplied expressions.
  • Properties that do not apply or are not known in a particular case are indicated by Missing[].
  • Properties include:
  • "AdditionFormulas"addition formulas
    "AlternativeRepresentations"alternative representations
    "ArgumentPattern"argument pattern
    "ArgumentSimplifications"argument simplifications
    "AsymptoticExpansions"asymptotic expansions
    "ComplexCharacteristics"complex characteristics
    "ContinuedFractionRepresentations"continued fraction representations
    "DifferenceEquations"difference equations
    "DifferentialEquations"differential equations
    "FourierTransforms"Fourier transforms
    "FractionalDerivatives"fractional derivatives
    "FunctionalEquations"functional equations
    "GeneratingFunctions"generating functions
    "HalfArgumentFormulas"halfargument formulas
    "HankelTransforms"Hankel transforms
    "HypergeometricRepresentations"hypergeometric representations
    "IntegralRepresentations"integral representations
    "InverseFourierTransforms"inverse Fourier transforms
    "InverseFunctionRelations"inverse function relations
    "LaplaceTransforms"Laplace transforms
    "LimitRepresentations"limit representations
    "MeijerGRepresentations"Meijer G representations
    "MellinTransforms"Mellin transforms
    "MultipliedArgumentFormulas"multipliedargument formulas
    "Name"function name
    "NamedIdentities"named identities
    "ParticularValues"particular values
    "ProductOfFunctionsFormulas"productoffunctions formulas
    "ProductRepresentations"product representations
    "ReflectionSymmetries"reflection symmetries
    "RelatedFunctionRepresentations"related function representations
    "RelatedFunctions"related functions
    "RelatedIdentities"related identities
    "RelatedInequalities"related inequalities
    "ResidueRepresentations"residue representations
    "SampleDefiniteIntegrals"sample definite integrals
    "SampleFiniteProducts"sample finite products
    "SampleFiniteSums"sample finite sums
    "SampleIndefiniteIntegrals"sample indefinite integrals
    "SampleInfiniteProducts"sample infinite products
    "SampleInfiniteSums"sample infinite sums
    "SeriesRepresentations"series representations
    "SummedTaylorSeriesLimits"summed Taylor series limits
    "SumOfFunctionsFormulas"sumoffunctions formulas
    "SymbolicDerivatives"symbolic derivatives
    "WolframFunctionsSiteLink"Wolfram Functions Site link
  • Some properties are available for MathematicalFunctionData as a whole and can be given using the form MathematicalFunctionData[property]. Such properties include:
  • "Entities"all available entities
    "EntityCount"total number of available entities
    "EntityCanonicalNames"list of all entity canonical names
    "SampleEntities"list of sample entities
    "EntityClasses"all available entity classes
    "EntityClassCount"total number of available entity classes
    "EntityClassCanonicalNames"list of all entity class canonical names
    "SampleEntityClasses"list of sample entity classes
    "Properties"all available properties
    "PropertyCount"total number of available properties
    "PropertyCanonicalNames"list of all property canonical names
    "PropertyClasses"all available property classes
    "PropertyClassCount"total number of available property classes
    "PropertyClassCanonicalNames"list of all property class canonical names
    "RandomEntity"pseudorandom sample entity
    "RandomEntities"list of 10 pseudorandom sample entities
    {"RandomEntities",n}n pseudorandom entities
    "RandomEntityClass"pseudorandom sample entity class
    "RandomEntityClasses"pseudorandom sample entity classes
    {"RandomEntityClasses",n}n pseudorandom entity classes
  • The following annotations can be used in the third argument of MathematicalFunctionData[entity,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
    "NonMissingEntities"list of entities for which the given property does not return Missing[]
    "NonMissingEntityAssociation"association of entities and entity-property values with entities returning Missing[] eliminated
    "EntityAssociation"an association of entities and entity-property values
    "PropertyAssociation"an association of properties and entity-property values

ExamplesExamplesopen allclose all

Basic Examples  (7)Basic Examples  (7)

Display known addition formulas for Sin:

Click for copyable input

Return integral representations for Sin:

Click for copyable input

Show argument simplifications for the incomplete elliptic integral of the second kind:

Click for copyable input

Give the residues of the binomial coefficient for symbolic arguments:

Click for copyable input

Return a list of sample function entities:

Click for copyable input

Return an entity association over an entity class:

Click for copyable input

Use e Ctrl+Equal to discover properties of a function:

Click for copyable input
Introduced in 2015