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Functions Induced by Iterated Deformed Laguerre Derivative: Analytical and Operational Approach

Author

Listed:
  • Sladjana D. Marinković
  • Miomir S. Stanković
  • Predrag M. Rajković

Abstract

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 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.

Suggested Citation

  • Sladjana D. Marinković & Miomir S. Stanković & Predrag M. Rajković, 2012. "Functions Induced by Iterated Deformed Laguerre Derivative: Analytical and Operational Approach," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:190726
    DOI: 10.1155/2012/190726
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    References listed on IDEAS

    as
    1. Martin Bohner & Allan Peterson, 2001. "Dynamic Equations on Time Scales," Springer Books, Springer, number 978-1-4612-0201-1, March.
    2. Borges, Ernesto P., 2004. "A possible deformed algebra and calculus inspired in nonextensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 95-101.
    3. G. Kaniadakis, 2009. "Maximum entropy principle and power-law tailed distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 3-13, July.
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