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q -Functions and Distributions, Operational and Umbral Methods

Author

Listed:
  • Giuseppe Dattoli

    (ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Rome, Italy
    The authors contributed to this work according to what is declared in the Author Contribution Section.)

  • Silvia Licciardi

    (ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Rome, Italy
    The authors contributed to this work according to what is declared in the Author Contribution Section.)

  • Bruna Germano

    (La Sapienza, Department of Methods and Mathematic Models for Applied Sciences, University of Rome, Via A. Scarpa, 14, 00161 Rome, Italy
    The authors contributed to this work according to what is declared in the Author Contribution Section.)

  • Maria Renata Martinelli

    (La Sapienza, Department of Methods and Mathematic Models for Applied Sciences, University of Rome, Via A. Scarpa, 14, 00161 Rome, Italy
    The authors contributed to this work according to what is declared in the Author Contribution Section.)

Abstract

The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials. These methods have helped to frame either elementary and special functions within the same logical context. Methods of Umbral and operational calculus have been embedded in a powerful and efficient analytical tool, which will be applied to the study of the properties of distributions such as Tsallis, Weibull and Student’s. We state that they can be viewed as standard Gaussian distributions and we take advantage of the relevant properties to infer those of the aforementioned distributions.

Suggested Citation

  • Giuseppe Dattoli & Silvia Licciardi & Bruna Germano & Maria Renata Martinelli, 2021. "q -Functions and Distributions, Operational and Umbral Methods," Mathematics, MDPI, vol. 9(21), pages 1-7, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2664-:d:661553
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