A New Representation of the Generalized Krätzel Function
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 definiti...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/11/2009 |
| _version_ | 1797548305507418112 |
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| author | Asifa Tassaddiq |
| author_facet | Asifa Tassaddiq |
| author_sort | Asifa Tassaddiq |
| collection | DOAJ |
| description | 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 <inline-formula><math display="inline"><semantics><mi>H</mi></semantics></math></inline-formula>-function is also explored to study new identities. |
| first_indexed | 2024-03-10T14:57:28Z |
| format | Article |
| id | doaj.art-fd5a501c591442398f8b736dc1cdc61d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:57:28Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-fd5a501c591442398f8b736dc1cdc61d2023-11-20T20:32:48ZengMDPI AGMathematics2227-73902020-11-01811200910.3390/math8112009A New Representation of the Generalized Krätzel FunctionAsifa Tassaddiq0Department of Basic Sciences and Humanities, College of Computer and Information Sciences Majmaah University, Al Majmaah 11952, Saudi ArabiaThe 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 <inline-formula><math display="inline"><semantics><mi>H</mi></semantics></math></inline-formula>-function is also explored to study new identities.https://www.mdpi.com/2227-7390/8/11/2009generalized Krätzel function<i>H</i>-functionFourier transformationslowly increasing test functionsgeneralized functions (distributions)delta function |
| spellingShingle | Asifa Tassaddiq A New Representation of the Generalized Krätzel Function Mathematics generalized Krätzel function <i>H</i>-function Fourier transformation slowly increasing test functions generalized functions (distributions) delta function |
| title | A New Representation of the Generalized Krätzel Function |
| title_full | A New Representation of the Generalized Krätzel Function |
| title_fullStr | A New Representation of the Generalized Krätzel Function |
| title_full_unstemmed | A New Representation of the Generalized Krätzel Function |
| title_short | A New Representation of the Generalized Krätzel Function |
| title_sort | new representation of the generalized kratzel function |
| topic | generalized Krätzel function <i>H</i>-function Fourier transformation slowly increasing test functions generalized functions (distributions) delta function |
| url | https://www.mdpi.com/2227-7390/8/11/2009 |
| work_keys_str_mv | AT asifatassaddiq anewrepresentationofthegeneralizedkratzelfunction AT asifatassaddiq newrepresentationofthegeneralizedkratzelfunction |