FunctionAdvisor/special_values - Maple Programming Help

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FunctionAdvisor/special_values

return the special values of a given mathematical function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

FunctionAdvisor(special_values, math_function)

Parameters

special_values

-

literal name; 'special_values'

math_function

-

Maple name of mathematical function

Description

• 

The FunctionAdvisor(special_values, math_function) command returns special values of the function computed at a selected list of special points.

Examples

FunctionAdvisorspecial_values,arccsc

arccsc−1=π2,arccsc233=π3,arccsc2=π4,arccsc−2=π6,arccsc2=π6,arccsc2=π4,arccsc233=π3,arccsc1=π2,arccscI=−Iln1+2,arccsc−I=Iln1+2,arccsc0=π2I,arccsc=0,arccsc=0

(1)

FunctionAdvisorspecial_values,sin

sinπ6=12,sinπ4=22,sinπ3=32,sin=undefined,sinI=I,sinπn=0,n::'integer',sin2n+1π2=−1,n::odd,sin2n+1π2=1,n::even

(2)

ex1FunctionAdvisorspecial_values,binomial

ex10z=1z=0sinπzπzotherwise,a0=1,a1=a,00=1

(3)

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.

dependsex1,a,dependsex1,z

false,false

(4)

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

ex2FunctionAdvisorspecial_values,binomiala,z

ex20z=1z=0sinπzπzotherwise,a0=1,a1=a,00=1

(5)

dependsex2,a,dependsex2,z

true,true

(6)

For functions which accept more than one argument, the special values of interest could be restricted by passing the function call. For example, these are special values for Ψ1,z

FunctionAdvisorspecial_values,Ψ1,z

Ψ−1,z=lnGAMMAzln2π2,Ψ1,1=π26,Ψ1,12=π22,Ψ1,14=π2+8Catalan,Ψ0,z=Ψz,Ψ1,−1=,Ψ1,0=,Ψ1,n=,Ψ1,n=π26k=1n11k2,Ψ1,n+12=π22k=1n42k12,Ψ1,12n=π22+k=1n42k12,n::'posint'

(7)

and these are special values for Ψz.

FunctionAdvisorspecial_values,Ψz

Ψ32=83γ2ln2&comma;Ψ12=2γ2ln2&comma;Ψ14=γ3ln2π2&comma;Ψ12=γ2ln2&comma;Ψ34=γ3ln2+π2&comma;Ψ13=γπ363ln32&comma;Ψ23=γ+π363ln32&comma;Ψ1=γ&comma;Ψ2=1γ&comma;Ψ−1=+I&comma;Ψ0=+I&comma;Ψ=&comma;Ψ=undefined&comma;ΨI=+Iπ2&comma;ΨI=Iπ2&comma;Ψn=k=1n11kγ&comma;n::&apos;posint&apos;&comma;Ψn+pq=qk=0n11kq+p+2k=1q212cos2πpkqlnsinπkqπcotπpq2ln2qγ&comma;Ψpqn=qk=0n11qk+1p+2k=1q212cos2πpkqlnsinπkqπcotπpq2ln2qγ&comma;n::&apos;nonnegint&apos;p&comma;q::set&apos;posint&apos;p<q

(8)

In these cases, when the FunctionAdvisor command is called with the function name, for example, Psi, the values are listed on the screen starting with those involving less arguments in the function call (in this example, Ψz).

See Also

depends

FunctionAdvisor

FunctionAdvisor/ branch_cuts

FunctionAdvisor/ branch_points

FunctionAdvisor/ identities

FunctionAdvisor/ topics

Psi