A New Representation of the Generalized Krätzel Function

Asifa Tassaddiq
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Asifa Tassaddiq: Department of Basic Sciences and Humanities, College of Computer and Information Sciences Majmaah University, Al Majmaah 11952, Saudi Arabia

Mathematics, 2020, vol. 8, issue 11, 1-17

Abstract: The confluence of distributions (generalized functions) with integral transforms has become a remarkably powerful tool to address important unsolved problems. The purpose of the present study is to investigate a distributional representation of the generalized Krätzel function. Hence, a new definition of these functions is formulated over a particular set of test functions. This is validated using the classical Fourier transform. The results lead to a novel extension of Krätzel functions by introducing distributions in terms of the delta function. A new version of the generalized Krätzel integral transform emerges as a natural consequence of this research. The relationship between the Krätzel function and the H -function is also explored to study new identities.

Keywords: generalized Krätzel function; H -function; Fourier transformation; slowly increasing test functions; generalized functions (distributions); delta function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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