Dear researchers,

I am considering the role of the Laplace transform for particular functions containing terms with csc(b(t)) (cosecant function with certain arguments b(t)), e.g., in dynamical systems theory or other areas.

My first concern is the function f(t) being regulated by the (Heaviside(t)-Heaviside(t-a)), a pulse with certain duration between 0 and a.

f(t) = log( csc(π*√(t)) )*(Heaviside(t)-Heaviside(t-a)). Eq.(1)

Where √t is the square root of t and log is the Natural logarithm.

I have discovered a way to calculate the Laplace transform of Eq.(1), which implies a long set of interesting expressions involving the Riemann zeta function and also de Bernoulli numbers and other important functions like the incomplete Gamma function. That is why I consider really important to link this result to dynamical system of linear behavior or where the Laplace transform of Eq. 1 can be used within a special context for some system.

Have you seen or revised some system or differential equation of a system containing terms like in f(t) = log( csc(π*√(t)) )*(Heaviside(t)-Heaviside(t-a)) ? That would be really appreciated if there is an unsolved problem in this direction involving the Laplace transform.

Best regards,

Carlos López