# MathematicalFunction

Named special functions.

Entity["MathematicalFunction",name] or

represents an entity of type "MathematicalFunction".

[prop]

gives the value of a specified property.

[{propi,}]

gives the value of a list of properties.

[prop,{qualivali,}]

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

EntityClass["MathematicalFunction",{propispeci,}]

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

# 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: