Poles and essential singularities

With respect to a

For Phi(z,s,a)

For Phi^{^}(z,s,a)

With respect to s

For Phi(z,s,a)

For Phi^{^}(z,s,a)

With respect to z

For Phi(z,s,a)

For Phi^{^}(z,s,a)