|
>
|
|
|
![[arccsc(-1) = -(1/2)*Pi, arccsc(-(2/3)*3^(1/2)) = -(1/3)*Pi, arccsc(-2^(1/2)) = -(1/4)*Pi, arccsc(-2) = -(1/6)*Pi, arccsc(2) = (1/6)*Pi, arccsc(2^(1/2)) = (1/4)*Pi, arccsc((2/3)*3^(1/2)) = (1/3)*Pi, arccsc(1) = (1/2)*Pi, arccsc(I) = -I*ln(1+2^(1/2)), arccsc(-I) = I*ln(1+2^(1/2)), arccsc(0) = (1/2)*Pi-infinity*I, arccsc(infinity) = 0, arccsc(-infinity) = 0]](/support/helpjp/helpview.aspx?si=7482/file01736/math58.png)
| (1) |
|
>
|
|
|
![[sin((1/6)*Pi) = 1/2, sin((1/4)*Pi) = (1/2)*2^(1/2), sin((1/3)*Pi) = (1/2)*3^(1/2), sin(infinity) = undefined, sin(infinity*I) = infinity*I, [sin(Pi*n) = 0, And(n::integer)], [sin((1/2)*(2*n+1)*Pi) = -1, And(n::odd)], [sin((1/2)*(2*n+1)*Pi) = 1, And(n::even)]]](/support/helpjp/helpview.aspx?si=7482/file01736/math65.png)
| (2) |
|
>
|
|
|
![[binomial(0, z) = piecewise(z = 0, 1, sin(Pi*z)/(Pi*z)), binomial(a, 0) = 1, binomial(a, 1) = a, binomial(0, 0) = 1]](/support/helpjp/helpview.aspx?si=7482/file01736/math72.png)
| (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.
|
>
|
![depends([ex1], a), depends([ex1], z)](/support/helpjp/helpview.aspx?si=7482/file01736/math87.png)
|
|
| (4) |
To make the FunctionAdvisor command return results using global variables, pass the function call itself.
|
>
|
|
|
![[binomial(0, z) = piecewise(z = 0, 1, sin(Pi*z)/(Pi*z)), binomial(a, 0) = 1, binomial(a, 1) = a, binomial(0, 0) = 1]](/support/helpjp/helpview.aspx?si=7482/file01736/math101.png)
| (5) |
|
>
|
![depends([ex2], a), depends([ex2], z)](/support/helpjp/helpview.aspx?si=7482/file01736/math105.png)
|
|
| (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 
|
>
|
|
|
![[Psi(-1, z) = lnGAMMA(z)-(1/2)*ln(2*Pi), Psi(1, 1) = (1/6)*Pi^2, Psi(1, 1/2) = (1/2)*Pi^2, Psi(1, 1/4) = 8*Catalan+Pi^2, Psi(0, z) = Psi(z), Psi(1, -1) = infinity, Psi(1, 0) = infinity, [Psi(1, -n) = infinity, Psi(1, n) = (1/6)*Pi^2-(Sum(1/k^2, k = 1 .. n-1)), Psi(1, n+1/2) = (1/2)*Pi^2-(Sum(4/(2*k-1)^2, k = 1 .. n)), Psi(1, 1/2-n) = (1/2)*Pi^2+Sum(4/(2*k-1)^2, k = 1 .. n), n::posint]]](/support/helpjp/helpview.aspx?si=7482/file01736/math118.png)
| (7) |
and these are special values for 
.
|
>
|
|
|
| (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, 
).
