On factorization of bicomplex meromorphic functions

Abstract

In this paper the factorization theory of meromorphic functions of one complex variable is promoted to bicomplex meromorphic functions. Many results of one complex variable case are seen to hold in bicomplex case, and it is found that there are results for meromorphic functions of one complex variable which are not true for bicomplex meromorphic functions. In particular, we show that for any bicomplex transcendental meromorphic function F, there exists a bicomplex meromorphic function G such that GF is prime even if the set: {a ε T : F(w) + aφ(w) is not prime} is empty or of cardinality N1 for any non-constant fractional linear bicomplex function φ. Moreover, as specific application, we obtain six additional possible forms of factorization of the complex cosine cos z in the bicomplex space.