Functions induced by iterated deformed Laguerre derivative: analytical and operational approach. (English) Zbl 1242.65028

Summary: The one-parameter deformed exponential function was introduced as a frame that enchases a few known functions of this type. Such deformation requires the corresponding deformed operations (addition and subtraction) and deformed operators (derivative and antiderivative). In this paper, we will demonstrate this theory in researching of some functions defined by an iterated deformed Laguerre operator. We study their properties, such as representation, orthogonality, generating function, differential and difference equation, and addition and summation formulas. Also, we consider these functions by the operational method.


65D15 Algorithms for approximation of functions
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