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Open AccessArticle

Mathematical Aspects of Krätzel Integral and Krätzel Transform

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Department of Mathematics and Statistics, McGill University, Montreal, PQ H3A 2K6, Canada
2
Office for Outer Space Affairs, United Nations, Vienna International Centre, A-1400 Vienna, Austria
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 526; https://doi.org/10.3390/math8040526
Received: 11 February 2020 / Revised: 17 March 2020 / Accepted: 22 March 2020 / Published: 3 April 2020
(This article belongs to the Special Issue Special Functions with Applications to Mathematical Physics)
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. View Full-Text
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 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
MDPI and ACS Style

Mathai, A.M.; Haubold, H.J. Mathematical Aspects of Krätzel Integral and Krätzel Transform. Mathematics 2020, 8, 526.

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