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An analogue of the Moyal star product is presented for the deformed oscillator algebra. It contains several homotopy-like additional integration parameters in the multiplication kernel generalizing the differential Moyal star-product formula exp[iεαβ∂^α ∂^β]. Using Pochhammer formula, integration over these parameters is carried over a Riemann surface associated with the expression of the type zˣ (1-z)ʸ where x and y are arbitrary real numbers.
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A. V. Korybut (2020) studied this question.
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