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Some properties of q-logarithm and q-exponential functions in Tsallis statistics

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  • Yamano, Takuya

Abstract

We present some formulae which q-logarithmic and q-exponential functions introduced in Tsallis statistics satisfy. Exact expression of the Mellin transform of q-exponential function is given. Moreover, the q-generalization of the digamma function is presented.

Suggested Citation

  • Yamano, Takuya, 2002. "Some properties of q-logarithm and q-exponential functions in Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(3), pages 486-496.
  • Handle: RePEc:eee:phsmap:v:305:y:2002:i:3:p:486-496
    DOI: 10.1016/S0378-4371(01)00567-2
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    Cited by:

    1. da Silva, G.B. & Ramos, R.V., 2019. "The Lambert–Tsallis Wq function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 164-170.
    2. Zhang, Fode & Ng, Hon Keung Tony & Shi, Yimin, 2018. "On alternative q-Weibull and q-extreme value distributions: Properties and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1171-1190.
    3. Koponen, Ismo T. & Palmgren, Elina & Keski-Vakkuri, Esko, 2021. "Characterising heavy-tailed networks using q-generalised entropy and q-adjacency kernels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    4. Zhang, Fode & Shi, Yimin & Wang, Ruibing, 2017. "Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 552-565.
    5. Takahashi, Taiki & Oono, Hidemi & Radford, Mark H.B., 2007. "Empirical estimation of consistency parameter in intertemporal choice based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 338-342.
    6. Dukkipati, Ambedkar & Murty, M. Narasimha & Bhatnagar, Shalabh, 2006. "Nonextensive triangle equality and other properties of Tsallis relative-entropy minimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 124-138.
    7. Soares, Abner D. & Moura Jr., Newton J. & Ribeiro, Marcelo B., 2016. "Tsallis statistics in the income distribution of Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 158-171.
    8. Rovenchak, Andrij & Sobko, Bohdana, 2019. "Fugacity versus chemical potential in nonadditive generalizations of the ideal Fermi-gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    9. Amelia Carolina Sparavigna, 2015. "Shannon, Tsallis And Kaniadakis Entropies In Bi-level Image Thresholding," International Journal of Sciences, Office ijSciences, vol. 4(02), pages 35-43, February.

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    Keywords

    Tsallis statistics;

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