A General Family of q-Hypergeometric Polynomials and Associated Generating Functions

Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of mathematical and physical sciences. Here, in t...

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Vydané v:	Mathematics (Basel) Ročník 9; číslo 11; s. 1161
Hlavní autori:	Srivastava, Hari Mohan, Arjika, Sama
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Basel MDPI AG 01.06.2021
Predmet:	Al-Salam-Carlitz q-polynomials basic (or q-) hypergeometric series cauchy polynomials homogeneous q-difference operator Hypergeometric functions Identities Investigations Mathematical analysis Physical sciences Polynomials q-binomial theorem rogers type formulas
ISSN:	2227-7390, 2227-7390
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Abstract	Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of mathematical and physical sciences. Here, in this paper, we introduce a general family of q-hypergeometric polynomials and investigate several q-series identities such as an extended generating function and a Srivastava-Agarwal type bilinear generating function for this family of q-hypergeometric polynomials. We give a transformational identity involving generating functions for the generalized q-hypergeometric polynomials which we have introduced here. We also point out relevant connections of the various q-results, which we investigate here, with those in several related earlier works on this subject. We conclude this paper by remarking that it will be a rather trivial and inconsequential exercise to give the so-called (p,q)-variations of the q-results, which we have investigated here, because the additional parameter p is obviously redundant.
AbstractList	Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of mathematical and physical sciences. Here, in this paper, we introduce a general family of q-hypergeometric polynomials and investigate several q-series identities such as an extended generating function and a Srivastava-Agarwal type bilinear generating function for this family of q-hypergeometric polynomials. We give a transformational identity involving generating functions for the generalized q-hypergeometric polynomials which we have introduced here. We also point out relevant connections of the various q-results, which we investigate here, with those in several related earlier works on this subject. We conclude this paper by remarking that it will be a rather trivial and inconsequential exercise to give the so-called (p,q)-variations of the q-results, which we have investigated here, because the additional parameter p is obviously redundant.
Author	Srivastava, Hari Mohan Arjika, Sama
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Cites_doi	10.1002/mana.19490020103 10.1016/j.jmaa.2012.05.088 10.3390/sym12111816 10.1007/s11139-015-9731-7 10.1007/BF01790345 10.1016/S0196-8858(03)00040-X 10.1111/sapm.12002 10.1002/mana.19490020504 10.1134/S1061920816010118 10.1002/mana.19650300105 10.1007/s11139-015-9676-x 10.1006/jcta.1997.2801 10.1186/s13662-020-03133-7 10.1186/s13662-020-02963-9 10.1007/s40995-019-00815-0 10.1002/mana.19490020604
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Copyright_xml	– notice: 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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References	Cao (ref_10) 2021; 12 Arjika (ref_21) 2021; 5 Srivastava (ref_6) 2020; 2 Cao (ref_24) 2012; 396 Srivastava (ref_27) 2020; 44 Srivastava (ref_17) 2020; 2020 Srivastava (ref_22) 2019; 1 Cao (ref_16) 2020; 2020 ref_19 Chen (ref_8) 1997; 80 Cao (ref_26) 2010; 217 Srivastava (ref_9) 2016; 23 Abdlhusein (ref_23) 2016; 40 Hahn (ref_13) 1949; 2 Cao (ref_20) 2016; 40 Chen (ref_5) 2003; 31 Cao (ref_15) 2013; 131 Srivastava (ref_25) 1989; 154 Hahn (ref_11) 1949; 2 ref_1 ref_3 Cao (ref_18) 2013; 219 ref_2 Hahn (ref_12) 1949; 2 Carlitz (ref_14) 1965; 30 Saad (ref_7) 2010; 215 ref_4
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SubjectTerms	Al-Salam-Carlitz q-polynomials basic (or q-) hypergeometric series cauchy polynomials homogeneous q-difference operator Hypergeometric functions Identities Investigations Mathematical analysis Physical sciences Polynomials q-binomial theorem rogers type formulas
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Title	A General Family of q-Hypergeometric Polynomials and Associated Generating Functions
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