MathematicalFunction

Named special functions.

Entity["MathematicalFunction",name] or

represents an entity of type "MathematicalFunction".

[prop]

gives the value of a specified property.

[{prop_i,…}]

gives the value of a list of properties.

[prop,{qual_ival_i,…}]

gives the value of a specified property modified by qualifier rules qual_i->val_i.

EntityClass["MathematicalFunction",{prop_ispec_i,…}]

represents a class of entities with values of prop_i defined by spec_i.

Sample Entities

Sample Entity Classes

Properties

	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
	EntityClasses	entity classes
	EntityTypeList	entity type list
	FourierTransforms	Fourier transforms
	FractionalDerivatives	fractional derivatives
	FunctionalEquations	functional equations
	GeneratingFunctions	generating functions
	HalfArgumentFormulas	half‐argument formulas
	HankelTransforms	Hankel transforms
	HypergeometricRepresentations	hypergeometric representations
	IntegralRepresentations	integral representations
	InverseFourierTransforms	inverse Fourier transforms
	InverseFunctionRelations	inverse function relations
	LaplaceTransforms	Laplace transforms
	LimitRepresentations	limit representations
	LowOrderDerivatives	low‐order derivatives
	MeijerGRepresentations
	MellinTransforms	Mellin transforms
	MultipliedArgumentFormulas	multiplied‐argument formulas
	Name	name
	NamedIdentities	named identities
	ParticularValues	particular values
	ProductOfFunctionsFormulas	product‐of‐functions 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	sum‐of‐functions formulas
	SymbolicDerivatives	symbolic derivatives
	TraditionalFormBoxes	traditional form boxes
	WolframFunctionsSiteLink	Wolfram Functions Site link
	Wronskians	Wronskians
	Zeros	zeros

Details

"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.

Examples

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:

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