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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

arccsc1=12π,arccsc233=13π,arccsc2=14π,arccsc2=16π,arccsc2=16π,arccsc2=14π,arccsc233=13π,arccsc1=12π,arccscI=Iln1+2,arccscI=Iln1+2,arccsc0=12π∞I,arccsc∞=0,arccsc∞=0

(1)

FunctionAdvisorspecial_values,sin

sin16π=12,sin14π=122,sin13π=123,sin∞=undefined,sin∞I=∞I,sinπn=0,Andn::integer,sin122n+1π=1,Andn::odd,sin122n+1π=1,Andn::even

(2)

ex1FunctionAdvisorspecial_values,binomial

ex1binomial0,z={1z=0sinπzπzotherwise,binomiala,0=1,binomiala,1=a,binomial0,0=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

ex2binomial0,z={1z=0sinπzπzotherwise,binomiala,0=1,binomiala,1=a,binomial0,0=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 Psi1,z

FunctionAdvisorspecial_values,Ψ1,z

Ψ1,z=lnGAMMAz12ln2π,Ψ1,1=16π2,Ψ1,12=12π2,Ψ1,14=π2+8Catalan,Ψ0,z=Ψz,Ψ1,1=∞,Ψ1,0=∞,Ψ1,n=∞,Ψ1,n=16π2k=1n11k2,Ψ1,n+12=12π2k=1n42k12,Ψ1,12n=12π2+k=1n42k12,n::posint

(7)

and these are special values for Psiz.

FunctionAdvisorspecial_values,Ψz

&Psi;32&equals;83&gamma;2ln2&comma;&Psi;12&equals;2&gamma;2ln2&comma;&Psi;14&equals;&gamma;3ln212&pi;&comma;&Psi;12&equals;&gamma;2ln2&comma;&Psi;34&equals;&gamma;3ln2&plus;12&pi;&comma;&Psi;13&equals;&gamma;16&pi;332ln3&comma;&Psi;23&equals;&gamma;&plus;16&pi;332ln3&comma;&Psi;1&equals;&gamma;&comma;&Psi;2&equals;1&gamma;&comma;&Psi;1&equals;&infin;&plus;&infin;I&comma;&Psi;0&equals;&infin;&plus;&infin;I&comma;&Psi;&infin;&equals;&infin;&comma;&Psi;&infin;&equals;undefined&comma;&Psi;&infin;I&equals;&infin;&plus;12I&pi;&comma;&Psi;&infin;I&equals;&infin;12I&pi;&comma;&Psi;n&equals;k&equals;1n11k&gamma;&comma;n::posint&comma;&Psi;n&plus;pq&equals;qk&equals;0n11kq&plus;p&plus;2k&equals;1floor12q12cos2&pi;pkqlnsin&pi;kq12&pi;cot&pi;pqln2q&gamma;&comma;&Psi;pqn&equals;qk&equals;0n11qk&plus;1p&plus;2k&equals;1floor12q12cos2&pi;pkqlnsin&pi;kq12&pi;cot&pi;pqln2q&gamma;&comma;n::nonnegintAndp&comma;q::setposintAndp<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, Psiz).

See Also

depends

FunctionAdvisor

FunctionAdvisor/ branch_cuts

FunctionAdvisor/ branch_points

FunctionAdvisor/ identities

FunctionAdvisor/ topics

Psi

 


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