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Mathematical Aspects of Krätzel Integral and Krätzel Transform

Author

Listed:
  • Arak M. Mathai

    (Department of Mathematics and Statistics, McGill University, Montreal, PQ H3A 2K6, Canada)

  • Hans J. Haubold

    (Office for Outer Space Affairs, United Nations, Vienna International Centre, A-1400 Vienna, Austria)

Abstract

A real scalar variable integral is known in the literature by different names in different disciplines. It is basically a Bessel integral called specifically Krätzel integral. An integral transform with this Krätzel function as kernel is known as Krätzel transform. This article examines some mathematical properties of Krätzel integral, its connection to Mellin convolutions and statistical distributions, its computable representations, and its extensions to multivariate and matrix-variate cases, in both the real and complex domains. An extension in the pathway family of functions is also explored.

Suggested Citation

  • Arak M. Mathai & Hans J. Haubold, 2020. "Mathematical Aspects of Krätzel Integral and Krätzel Transform," Mathematics, MDPI, vol. 8(4), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:526-:d:340993
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    References listed on IDEAS

    as
    1. Mathai, A.M. & Haubold, H.J., 2007. "Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 110-122.
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