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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| Vydáno v: | Symmetry (Basel) Ročník 12; číslo 11; s. 1816 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
01.11.2020
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| ISSN: | 2073-8994, 2073-8994 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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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| ISSN: | 2073-8994 2073-8994 |
| DOI: | 10.3390/sym12111816 |