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In this article we study the concept of pq-functions which should be regarded as an extension of prior work relating to pq-radial functions. Here, our main aim is to generalize this concept to the field of complex numbers. As direct consequences, new kind of (partial) DEs, polynomials, series and integrals are derived; Joukowski function and Legendre polynomials are generalized; the relationships between pq-DEs and DEs of Fuchs class, and DEs of Sturm-Liouville form are investigated.doi:10.6084/m9.figshare.3376339 fatcat:yg4gmwlptrdd5jxkhefbbzsbgy