Mathematical Aspects of Krätzel Integral and Krätzel Transform
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 mathema...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/4/526 |
| _version_ | 1797571556446044160 |
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| author | Arak M. Mathai Hans J. Haubold |
| author_facet | Arak M. Mathai Hans J. Haubold |
| author_sort | Arak M. Mathai |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T20:42:10Z |
| format | Article |
| id | doaj.art-9bff2c7aa14e4671a8773ca407798d1b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:42:10Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9bff2c7aa14e4671a8773ca407798d1b2023-11-19T20:36:38ZengMDPI AGMathematics2227-73902020-04-018452610.3390/math8040526Mathematical Aspects of Krätzel Integral and Krätzel TransformArak M. Mathai0Hans J. Haubold1Department of Mathematics and Statistics, McGill University, Montreal, PQ H3A 2K6, CanadaOffice for Outer Space Affairs, United Nations, Vienna International Centre, A-1400 Vienna, AustriaA 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.https://www.mdpi.com/2227-7390/8/4/526Mellin convolutionsKrätzel integralsreaction-rate probability integralcontinuous mixturesBayesian structuresfractional integrals |
| spellingShingle | Arak M. Mathai Hans J. Haubold Mathematical Aspects of Krätzel Integral and Krätzel Transform Mathematics Mellin convolutions Krätzel integrals reaction-rate probability integral continuous mixtures Bayesian structures fractional integrals |
| title | Mathematical Aspects of Krätzel Integral and Krätzel Transform |
| title_full | Mathematical Aspects of Krätzel Integral and Krätzel Transform |
| title_fullStr | Mathematical Aspects of Krätzel Integral and Krätzel Transform |
| title_full_unstemmed | Mathematical Aspects of Krätzel Integral and Krätzel Transform |
| title_short | Mathematical Aspects of Krätzel Integral and Krätzel Transform |
| title_sort | mathematical aspects of kratzel integral and kratzel transform |
| topic | Mellin convolutions Krätzel integrals reaction-rate probability integral continuous mixtures Bayesian structures fractional integrals |
| url | https://www.mdpi.com/2227-7390/8/4/526 |
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