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FunctionAdvisor/relate

relate the two given mathematical functions

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

FunctionAdvisor(relate, math_function_1, math_function_2)

Parameters

relate

-

literal name; 'relate'

math_function_1

-

Maple name of first mathematical function

math_function_2

-

Maple name of second mathematical function

Description

• 

The FunctionAdvisor(relate, math_function_1, math_function_2) command attempts to relate the functions using the internal Maple algorithms. For more information, see convert[to_special_function].

  

By default, the output has the simpler or more standard function on the left-hand side. This topic is similar to FunctionAdvisor/specialize, which allows you to specify which function is expressed in terms of the other one. This typically requires additional constraints in the function parameter(s) domain(s).

Examples

FunctionAdvisorrelate,sin,WhittakerM

sinz=12IWhittakerM0,12,2Iz

(1)

FunctionAdvisorrelate,KummerU,BesselK

BesselKa,z=π2zaKummerUa+12,2a+1,2zⅇz

(2)

FunctionAdvisorrelate,HermiteH,erf

erfz=2HermiteH1,zπⅇz2+1

(3)

FunctionAdvisorrelate,HermiteH,LaguerreL

HermiteHa,z=2aπLaguerreL12a,12,z2binomial12+12a,12aΓ1212a2zLaguerreL12+12a,12,z2binomial12a,12+12aΓ12a

(4)

Notice that a relation between KummerU and HermiteH does not exist for arbitrary values of their parameters.

FunctionAdvisorrelate,KummerU,Hermite

* Partial match of Hermite against topic HermiteH.
Unable to establish a relation between KummerU and HermiteH

However, that relation does exist for a specialization of the function parameters

FunctionAdvisorspecialize,KummerU,HermiteH

KummerUa,b,z=HermiteH2a,z22a,Andb=12,KummerUa,b,z=12HermiteH2a+1,z22az,Andb=32

(5)

and also the converse.

ex1FunctionAdvisorspecialize,HermiteH,KummerU

ex1:=HermiteHa&comma;z&equals;2aKummerU12a&comma;12&comma;z2&comma;And0<&real;zorAnd&real;z&equals;0&comma;0<&Im;z

(6)

The variables used by the FunctionAdvisor command to create the function calling sequences are local variables. Therefore, the previous example does not depend on z.

dependsex1&comma;a&comma;dependsex1&comma;b&comma;dependsex1&comma;z

false&comma;false&comma;false

(7)

To make the FunctionAdvisor command return results using global variables, pass the function call itself.

ex2FunctionAdvisorspecialize&comma;HermiteHa&comma;z&comma;KummerU

ex2:=HermiteHa&comma;z&equals;2aKummerU12a&comma;12&comma;z2&comma;And0<&real;zorAnd&real;z&equals;0&comma;0<&Im;z

(8)

dependsex2&comma;a&comma;dependsex2&comma;b&comma;dependsex2&comma;z

true&comma;false&comma;true

(9)

You can view the default hierarchy used when calling the FunctionAdvisor command with the keyword relate as first argument using the following

`convert/to_special_function/hierarchy`function

sin&comma;cos&comma;tan&comma;csc&comma;sec&comma;cot&comma;sinh&comma;cosh&comma;tanh&comma;csch&comma;sech&comma;coth&comma;arcsin&comma;arccos&comma;arctan&comma;arccsc&comma;arcsec&comma;arccot&comma;arcsinh&comma;arccosh&comma;arctanh&comma;arccsch&comma;arcsech&comma;arccoth&comma;exp&comma;ln&comma;&Gamma;&comma;lnGAMMA&comma;factorial&comma;binomial&comma;multinomial&comma;&Beta;&comma;pochhammer&comma;doublefactorial&comma;&Psi;&comma;harmonic&comma;KelvinBer&comma;KelvinBei&comma;KelvinKer&comma;KelvinKei&comma;KelvinHer&comma;KelvinHei&comma;AiryAi&comma;AiryBi&comma;HankelH1&comma;HankelH2&comma;BesselI&comma;BesselJ&comma;BesselK&comma;BesselY&comma;Sum&comma;sum&comma;GegenbauerC&comma;HermiteH&comma;LaguerreL&comma;LegendreP&comma;ChebyshevT&comma;ChebyshevU&comma;JacobiP&comma;Ei&comma;Li&comma;Si&comma;Shi&comma;Ci&comma;Chi&comma;Ssi&comma;erf&comma;erfc&comma;erfi&comma;FresnelC&comma;FresnelS&comma;Fresnelf&comma;Fresnelg&comma;dawson&comma;KummerM&comma;KummerU&comma;WhittakerM&comma;WhittakerW&comma;CylinderD&comma;CylinderU&comma;CylinderV&comma;CoulombF&comma;EllipticE&comma;EllipticCE&comma;EllipticF&comma;InverseJacobiSN&comma;InverseJacobiAM&comma;EllipticK&comma;EllipticCK&comma;EllipticPi&comma;EllipticCPi&comma;EllipticModulus&comma;EllipticNome&comma;LegendreQ&comma;SphericalY&comma;LerchPhi&comma;GaussAGM&comma;LommelS1&comma;MeijerG&comma;hypergeom&comma;Hypergeom&comma;Sum&comma;sum&comma;LommelS2&comma;StruveH&comma;StruveL&comma;AngerJ&comma;WeberE&comma;dilog&comma;polylog&comma;JacobiAM&comma;JacobiSN&comma;JacobiCN&comma;JacobiDN&comma;JacobiNS&comma;JacobiNC&comma;JacobiND&comma;JacobiSC&comma;JacobiCS&comma;JacobiSD&comma;JacobiDS&comma;JacobiCD&comma;JacobiDC&comma;JacobiTheta1&comma;JacobiTheta2&comma;JacobiTheta3&comma;JacobiTheta4&comma;JacobiZeta&comma;InverseJacobiCN&comma;InverseJacobiDN&comma;InverseJacobiNS&comma;InverseJacobiNC&comma;InverseJacobiND&comma;InverseJacobiSC&comma;InverseJacobiCS&comma;InverseJacobiSD&comma;InverseJacobiDS&comma;InverseJacobiCD&comma;InverseJacobiDC&comma;WeierstrassP&comma;WeierstrassPPrime&comma;WeierstrassZeta&comma;WeierstrassSigma&comma;&zeta;&comma;abs&comma;conjugate&comma;&real;&comma;&Im;&comma;argument&comma;signum&comma;Dirac&comma;Heaviside&comma;max&comma;min&comma;piecewise&comma;LambertW&comma;Wrightomega&comma;unwindK&comma;euler&comma;bernoulli&comma;Stirling1&comma;Stirling2&comma;BellB&comma;CompleteBellB&comma;IncompleteBellB&comma;HeunT&comma;HeunB&comma;HeunD&comma;HeunC&comma;HeunG&comma;HeunTPrime&comma;HeunBPrime&comma;HeunDPrime&comma;HeunCPrime&comma;HeunGPrime&comma;MathieuC&comma;MathieuCPrime&comma;MathieuS&comma;MathieuSPrime&comma;MathieuCE&comma;MathieuCEPrime&comma;MathieuSE&comma;MathieuSEPrime&comma;MathieuFloquet&comma;MathieuFloquetPrime&comma;MathieuA&comma;MathieuB&comma;MathieuExponent&comma;fourier&comma;invfourier&comma;fouriercos&comma;fouriersin&comma;hankel&comma;hilbert&comma;invhilbert&comma;laplace&comma;invlaplace&comma;mellin&comma;invmellin

(10)

where functions to the left are selected before functions to the right when constructing the left-hand side of the output.

See Also

convert/to_special_function

depends

FunctionAdvisor

FunctionAdvisor/specialize

FunctionAdvisor/topics

HermiteH

KummerU

 


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