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By introducing the hierarchy of Fibonacci divisors and corresponding quantumderivatives, we develop the golden calculus, hierarchy of golden binomials andrelated exponential functions, translation operator and infinite hierarchy ofGolden analytic functions. The hierarchy of Golden periodic functions,appearing in this calculus we relate with the method of images in planarhydrodynamics for incompressible and irrotational flow in bounded domain. Weshow that the even hierarchy of these functions determine the flow in theannular domain, bounded by concentric circles with the ratio of radiuses inpowers of the Golden ratio. As an example, complex potential and velocity fieldfor the set of point vortices with Golden proportion of images are calculatedexplicitly.

PQ-Calculus of Fibonacci Divisors and Method of Images in Planar Hydrodynamics