Coherent states with complex functions

Abstract

The canonical coherent states are expressed as infinite series in powers of a complex number $z$ in their infinite series version. In this article we present classes of coherent states by replacing this complex number $z$ by other choices, namely, iterates of a complex function, higher functions and elementary functions. Further, we show that some of these classes do not furnish generalized oscillator algebras in the natural way. A reproducing kernel Hilbert space is discussed to each class of coherent states.