A Note on Generalized q-Difference Equations and Their Applications Involving q-Hypergeometric Functions
Our investigation is motivated essentially by the demonstrated applications of the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and basic (or q-) hypergeometric polynomials, in many diverse areas. Here, in this paper, we use two q-operator...
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| Veröffentlicht in: | Symmetry (Basel) Jg. 12; H. 11; S. 1816 |
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01.11.2020
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| Abstract | Our investigation is motivated essentially by the demonstrated applications of the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and basic (or q-) hypergeometric polynomials, in many diverse areas. Here, in this paper, we use two q-operators T(a,b,c,d,e,yDx) and E(a,b,c,d,e,yθx) to derive two potentially useful generalizations of the q-binomial theorem, a set of two extensions of the q-Chu-Vandermonde summation formula and two new generalizations of the Andrews-Askey integral by means of the q-difference equations. We also briefly describe relevant connections of various special cases and consequences of our main results with a number of known results. |
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| AbstractList | Our investigation is motivated essentially by the demonstrated applications of the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and basic (or q-) hypergeometric polynomials, in many diverse areas. Here, in this paper, we use two q-operators T(a,b,c,d,e,yDx) and E(a,b,c,d,e,yθx) to derive two potentially useful generalizations of the q-binomial theorem, a set of two extensions of the q-Chu-Vandermonde summation formula and two new generalizations of the Andrews-Askey integral by means of the q-difference equations. We also briefly describe relevant connections of various special cases and consequences of our main results with a number of known results. |
| Author | Arjika, Sama Srivastava, Hari M. Cao, Jian |
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| Cites_doi | 10.1090/cbms/066 10.1139/cjp-2012-0403 10.1093/imamat/33.2.205 10.1006/jcta.1997.2801 10.3390/sym12061043 10.1016/j.amc.2013.01.065 10.1080/10236190902810385 10.1007/s40995-019-00815-0 10.1080/10236198.2020.1804888 10.1080/10236190903530735 10.25073/jaec.201931.229 10.1134/S1061920816010118 10.1515/caim-2017-0009 10.1016/j.aam.2007.08.001 10.1093/imamat/30.3.315 10.1186/s13662-016-0741-6 10.1016/S0196-8858(03)00040-X 10.4134/JKMS.2010.47.2.223 10.1016/j.jmaa.2013.11.027 10.1016/0022-247X(82)90154-8 10.1134/S0016793217050140 10.1007/978-1-4612-4108-9 10.1016/j.amc.2009.12.061 10.1016/B978-0-12-385218-2.00002-5 10.1186/s13662-020-02963-9 10.1186/s13662-020-03133-7 |
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