Mathematical Aspects of Krätzel Integral and Krätzel Transform

Arak M. Mathai and Hans J. Haubold
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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

Mathematics, 2020, vol. 8, issue 4, 1-18

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.

Keywords: Mellin convolutions; Krätzel integrals; reaction-rate probability integral; continuous mixtures; Bayesian structures; fractional integrals; statistical distribution of products and ratios; multivariate and matrix-variate cases; real and complex domains (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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