FunctionAdvisor/identities - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : FunctionAdvisor : FunctionAdvisor/identities

FunctionAdvisor/identities

return the identities of a given mathematical function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

FunctionAdvisor(identities, math_function)

Parameters

identities

-

literal name; 'identities'

math_function

-

Maple name of mathematical function

Description

• 

The FunctionAdvisor(identities, math_function) command returns a list of identities for that function.

Examples

FunctionAdvisoridentities,sin

sinarcsinz=z,sinz=sinz,sinz=2sin12zcos12z,sinz=1cscz,sinz=2tan12z1+tan12z2,sinz=12IⅇIzⅇIz,sinz2=1cosz2,sinz2=1212cos2z

(1)

FunctionAdvisordescribe,coth

coth=hyperbolic cotangent

(2)

FunctionAdvisordefinition,coth

cothz=ⅇz2+1ⅇz21,with no restrictions on z

(3)

FunctionAdvisoridentities,coth

cothz=cothz,cothz=12coth12z21coth12z,cothz=coshzsinhz,cothz=1+cosh2zsinh2z,cothz=sinh2z1cosh2z,cothz=1tanhz,cothz=121+tanh12z2tanh12z,cothz=I12Icoth12z12Itanh12z,cothz=ⅇz+ⅇzⅇzⅇz,cothz=IIcsch2zIcoth2z

(4)

eq1FunctionAdvisoridentities,BesselI

eq1BesselIa,z=zaBesselIa,zza,BesselIa,Iz=IzaBesselJa,zza,BesselIa+1,zBesselIa,zBesselI1a,zBesselIa,z=2sinπaπz,BesselIa,z2=z212aBesselIa,zza,BesselIa,bczqp=bczqpaBesselIa,bcpzpqbcpzpqa,And2p::integer,BesselIa,z=2a1BesselIa1,zz+BesselIa2,z,BesselIa,z=2a+1BesselIa+1,zz+BesselIa+2,z

(5)

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

dependseq1,a,dependseq1,z

false,false

(6)

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

eq2FunctionAdvisoridentities,Eia,z

eq2Ei1,z=Eiz+12lnz12ln1zlnz,Eia,z=a!ⅇz_k1=0az_k1a1_k1!,Anda::nonnegint,Eia,z=zEi2+a,z+2+azEi1+a,z1+a,Eia,z=a+zEi1+a,z+1+aEi2+a,zz

(7)

dependseq2,a,dependseq2,z

true,true

(8)

See Also

depends

FunctionAdvisor

FunctionAdvisor/special_values

FunctionAdvisor/topics

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam