MathematicalFunctionData

For general access to the Wolfram Knowledgebase, use entities of type MathematicalFunction instead of MathematicalFunctionData.

MathematicalFunctionData[entity,property]

gives data corresponding to property for the mathematical function specified by entity.

MathematicalFunctionData[entprop,annotation]

gives data corresponding to the given entity or property in the format specified by annotation.

MathematicalFunctionData[entity,property,annotation]

gives data for the given entity-property pair in the format specified by annotation.    

MathematicalFunctionData[entity,property,{qual1val1,qual2val2,}]

gives data for the given entity-property pair with property qualifiers qual1, qual2, set to the given values.

MathematicalFunctionData[entity,property,annotation,{qual1val1,qual2val2,}]

gives data corresponding to the given entity, property, and annotation format, with property qualifiers qual1, qual2, set to the given values.

Details

  • MathematicalFunctionData can be used to access identities involving mathematical functions.
  • MathematicalFunctionData[] or MathematicalFunctionData["Entities"] gives a list of available mathematical function entities.
  • MathematicalFunctionData["Properties"] gives a list of available properties.
  • The specified entity in MathematicalFunctionData can be an Entity, EntityClass, entity canonical name or list of entities.
  • 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
    "Classes"classes
    "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
    "LowOrderDerivates"loworder derivatives
    "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
    "Residues"residues
    "SampleDefiniteIntegrals"sample definite integrals
    "SampleFiniteProducts"sample finite products
    "SampleFiniteSums"sample finite sums
    "SampleIndefiniteIntegrals"sample indefinite integrals
    "SampleInfiniteProducts"sample infinite products
    "SampleInfiniteSums"sample infinite sums
    "SampleIntegrals"sample integrals
    "SeriesRepresentations"series representations
    "SummedTaylorSeriesLimits"summed Taylor series limits
    "SumOfFunctionsFormulas"sumoffunctions formulas
    "SymbolicDerivatives"symbolic derivatives
    "TraditionalFormBoxes"traditional form boxes
    "WolframFunctionsSiteLink"Wolfram Functions Site link
    "Wronskians"Wronskians
    "Zeros"zeros
  • Some data is available for MathematicalFunctionData as a whole and can be given using the form MathematicalFunctionData[property]. Such domainlevel 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 annotation strings can be used in the second or third argument of MathematicalFunctionData, where applicable, to specify in which format the data should be returned:
  • "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
    "NonMissingEntities"a list of entities for which the given property does not return Missing[]
    "NonMissingProperties"a list of properties for which the given entity does not return Missing[]
    "NonMissingEntityAssociation"an association of entities and entity-property values with entities returning Missing[] eliminated
    "NonMissingPropertyAssociation"an association of entities and entity-property values with properties returning Missing[] eliminated
  • MathematicalFunctionData[EntityProperty[],subproperty] can be used to lookup up property metadata. Available metadata strings that can be used in the second argument are:
  • "Description"a textual definition of the property
    "Label"the label of the property
    "Qualifiers"the list of possible qualifiers for the property
  • MathematicalFunctionData relies on the internet to retrieve data from the Wolfram servers.

Examples

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Basic Examples  (8)

Display known addition formulas for Sin:

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Return integral representations for Sin:

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

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Give the residues of the binomial coefficient for symbolic arguments:

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Return a list of sample function entities:

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Return an entity association over an entity class:

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Return identities corresponding to an external cross-reference, if available:

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Use to discover properties of a function:

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Scope  (7)

Generalizations & Extensions  (1)

Applications  (2)

Properties & Relations  (3)

Possible Issues  (2)

Introduced in 2015
(10.3)
|
Updated in 2019
(12.0)