FunctionAdvisor/relate
relate the two given mathematical functions
Calling Sequence
Parameters
Description
Examples
FunctionAdvisor(relate, math_function_1, math_function_2)
relate
-
literal name; 'relate'
math_function_1
Maple name of first mathematical function
math_function_2
Maple name of second mathematical function
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).
FunctionAdvisorrelate,sin,WhittakerM
sinz=−I2WhittakerM0,12,2Iz
FunctionAdvisorrelate,KummerU,BesselK
BesselKa,z=π2zaKummerUa+12,2a+1,2zⅇz
FunctionAdvisorrelate,HermiteH,erf
erfz=−2HermiteH−1,zπⅇz2+1
FunctionAdvisorrelate,HermiteH,LaguerreL
HermiteHa,z=2aπLaguerreLa2,−12,z2−12+a2a2Γ12−a2−2zLaguerreL−12+a2,12,z2a2−12+a2Γ−a2
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=HermiteH−2a,z22a,b=12,KummerUa,b,z=HermiteH−2a+1,z22a2z,b=32
and also the converse.
ex1≔FunctionAdvisorspecialize,HermiteH,KummerU
ex1≔HermiteHa,z=2aKummerU−a2,12,z2,0<ℜz∨ℜz=0∧0<ℑz
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,a,dependsex1,b,dependsex1,z
false,false,false
To make the FunctionAdvisor command return results using global variables, pass the function call itself.
ex2≔FunctionAdvisorspecialize,HermiteHa,z,KummerU
ex2≔HermiteHa,z=2aKummerU−a2,12,z2,0<ℜz∨ℜz=0∧0<ℑz
dependsex2,a,dependsex2,b,dependsex2,z
true,false,true
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,cos,tan,csc,sec,cot,sinh,cosh,tanh,csch,sech,coth,arcsin,arccos,arctan,arccsc,arcsec,arccot,arcsinh,arccosh,arctanh,arccsch,arcsech,arccoth,exp,ln,Γ,lnGAMMA,factorial,binomial,multinomial,Β,pochhammer,doublefactorial,Ψ,harmonic,KelvinBer,KelvinBei,KelvinKer,KelvinKei,KelvinHer,KelvinHei,AiryAi,AiryBi,HankelH1,HankelH2,BesselI,BesselJ,BesselK,BesselY,GegenbauerC,HermiteH,LaguerreL,LegendreP,ChebyshevT,ChebyshevU,JacobiP,Ei,Li,Si,Shi,Ci,Chi,Ssi,erf,erfc,erfi,FresnelC,FresnelS,Fresnelf,Fresnelg,dawson,KummerM,KummerU,WhittakerM,WhittakerW,CylinderD,CylinderU,CylinderV,CoulombF,EllipticE,EllipticCE,EllipticF,InverseJacobiSN,InverseJacobiAM,EllipticK,EllipticCK,EllipticPi,EllipticCPi,EllipticModulus,EllipticNome,LegendreQ,SphericalY,LerchPhi,GaussAGM,LommelS1,MeijerG,hypergeom,Hypergeom,AppellF1,AppellF2,AppellF3,AppellF4,Sum,sum,LommelS2,StruveH,StruveL,AngerJ,WeberE,dilog,polylog,JacobiAM,JacobiSN,JacobiCN,JacobiDN,JacobiNS,JacobiNC,JacobiND,JacobiSC,JacobiCS,JacobiSD,JacobiDS,JacobiCD,JacobiDC,JacobiTheta1,JacobiTheta2,JacobiTheta3,JacobiTheta4,JacobiZeta,InverseJacobiCN,InverseJacobiDN,InverseJacobiNS,InverseJacobiNC,InverseJacobiND,InverseJacobiSC,InverseJacobiCS,InverseJacobiSD,InverseJacobiDS,InverseJacobiCD,InverseJacobiDC,WeierstrassP,WeierstrassPPrime,WeierstrassZeta,WeierstrassSigma,Ζ,abs,conjugate,ℜ,ℑ,argument,signum,Dirac,Heaviside,max,min,piecewise,LambertW,Wrightomega,unwindK,euler,bernoulli,Stirling1,Stirling2,BellB,CompleteBellB,IncompleteBellB,HeunT,HeunB,HeunD,HeunC,HeunG,HeunTPrime,HeunBPrime,HeunDPrime,HeunCPrime,HeunGPrime,MathieuC,MathieuCPrime,MathieuS,MathieuSPrime,MathieuCE,MathieuCEPrime,MathieuSE,MathieuSEPrime,MathieuFloquet,MathieuFloquetPrime,MathieuA,MathieuB,MathieuExponent,GeneralizedPolylog,MultiPolylog,MultiZeta,NielsenPolylog,fourier,invfourier,fouriercos,fouriersin,hankel,hilbert,invhilbert,laplace,invlaplace,mellin,invmellin
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
Download Help Document
