What Are the Special Names for These Functions?

[Jhenrique]

I'd like of know if the following functions have name: Y(σ), H(σ) X(σ), Y(iω), X(iω), Y(s), X(s).

PS, I suppose that H(σ) must be the "exponential response"...

 

[TheFerruccio]

Is there a context for these? They can be called whatever you'd like to call them without context.

 

[AlephZero]

Y and H are usually types of Bessel functions, but I don't recognize X as a standard notation for anything.

 

[Mark44]

Without some context we can't give any definitive answers. H is also used for the Heaviside step function. Y(s) is used for the Laplace transform of some function y(t). Same for X(s), but in this context, x, y, X, and Y are just function names with no special meaning.

 

[Jhenrique]

oooh sorry... in the context of Control Theory: https://en.wikipedia.org/wiki/Transfer_function, https://en.wikipedia.org/wiki/Proper_transfer_function

 

[HallsofIvy]

I'd like of know if the following functions have name: Y(σ), H(σ) X(σ), Y(iω), X(iω), Y(s), X(s).

PS, I suppose that H(σ) must be the "exponential response"...

Those are all defined in the first page you cite. "X" is the Laplace transform of whatever "input function" you have and "Y" is the Laplace transform of its "output function". H is the ratio $\frac{Y}{X}$.

 

[Jhenrique]

Not always those functions has the same name, for example, h(t) = "impulse function", H(s) = "transfer function" and H(iω) = "frequency response". For this I asked if the functions in my first post have special names...