Derivatives of any Horn-type hypergeometric functions with respect to their parameters
We consider the derivatives of Horn hypergeometric functions of any number of variables with respect to their parameters. The derivative of such a function of n variables is expressed as a Horn hypergeometric series of n+1 infinite summations depending on the same variables and with the same region...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-03-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321319303979 |
| _version_ | 1828524968329084928 |
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| author | Vladimir V. Bytev Bernd A. Kniehl |
| author_facet | Vladimir V. Bytev Bernd A. Kniehl |
| author_sort | Vladimir V. Bytev |
| collection | DOAJ |
| description | We consider the derivatives of Horn hypergeometric functions of any number of variables with respect to their parameters. The derivative of such a function of n variables is expressed as a Horn hypergeometric series of n+1 infinite summations depending on the same variables and with the same region of convergence as for the original Horn hypergeometric function. The derivatives of Appell functions, generalized hypergeometric functions, confluent and non-confluent Lauricella series, and generalized Lauricella series are explicitly presented. Applications to the calculations of Feynman diagrams are discussed, especially the series expansions in ϵ within dimensional regularization. Connections with other classes of special functions are discussed as well. |
| first_indexed | 2024-12-11T20:57:18Z |
| format | Article |
| id | doaj.art-5d71b37e8a97451492b6c40c2231892b |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-11T20:57:18Z |
| publishDate | 2020-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-5d71b37e8a97451492b6c40c2231892b2022-12-22T00:51:04ZengElsevierNuclear Physics B0550-32132020-03-01952Derivatives of any Horn-type hypergeometric functions with respect to their parametersVladimir V. Bytev0Bernd A. Kniehl1II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany; Joint Institute for Nuclear Research, 141980 Dubna (Moscow Region), RussiaII. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany; Corresponding author.We consider the derivatives of Horn hypergeometric functions of any number of variables with respect to their parameters. The derivative of such a function of n variables is expressed as a Horn hypergeometric series of n+1 infinite summations depending on the same variables and with the same region of convergence as for the original Horn hypergeometric function. The derivatives of Appell functions, generalized hypergeometric functions, confluent and non-confluent Lauricella series, and generalized Lauricella series are explicitly presented. Applications to the calculations of Feynman diagrams are discussed, especially the series expansions in ϵ within dimensional regularization. Connections with other classes of special functions are discussed as well.http://www.sciencedirect.com/science/article/pii/S0550321319303979 |
| spellingShingle | Vladimir V. Bytev Bernd A. Kniehl Derivatives of any Horn-type hypergeometric functions with respect to their parameters Nuclear Physics B |
| title | Derivatives of any Horn-type hypergeometric functions with respect to their parameters |
| title_full | Derivatives of any Horn-type hypergeometric functions with respect to their parameters |
| title_fullStr | Derivatives of any Horn-type hypergeometric functions with respect to their parameters |
| title_full_unstemmed | Derivatives of any Horn-type hypergeometric functions with respect to their parameters |
| title_short | Derivatives of any Horn-type hypergeometric functions with respect to their parameters |
| title_sort | derivatives of any horn type hypergeometric functions with respect to their parameters |
| url | http://www.sciencedirect.com/science/article/pii/S0550321319303979 |
| work_keys_str_mv | AT vladimirvbytev derivativesofanyhorntypehypergeometricfunctionswithrespecttotheirparameters AT berndakniehl derivativesofanyhorntypehypergeometricfunctionswithrespecttotheirparameters |