Modular forms and k-colored generalized Frobenius partitions

Let k and n be positive integers. Let c ₊ (n) denote the number of k-colored generalized Frobenius partitions of n and let C ₖ (q) be the generating function of c ₊ (n). In this article, we study C ₖ (q) using the theory of modular forms and discover new surprising properties of C ₖ (q).