A new class of the entire functions: a study of two cases from Euler

In this article an alternative infinite product for a special class of the entire functions are studied by using some results of the Laguerre-P\'{o}lya entire functions. The zeros for a class of the special even entire functions are discussed in detail. It is proved that the infinite product and series representations for the hyperbolic and trigonometric cosine functions, which are coming from Euler, are our special cases.Comment: 10 page