On intermediate q-Lauricella functions in the spirit of Karlsson, Chandel Singh and Gupta

Thomas Ernst

Abstract


The purpose of this article is to define some intermediate q-Lauricella functions, to find convergence regions in two different forms, and to prove corresponding reduction formulas by using a known lemma from our first book. These convergence regions are given in form of q-additions and q-real numbers. The third q-real number plays a special role in the computations. Generating functions are proved by using the q-binomial theorem. Finally, special cases of q-Lauricella functions as well as confluent forms in the spirit of Chandel Singh and Gupta are given.

Keywords


Intermediate q-Lauricella function; convergence region; q-additions; generating function

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References


Chandel Singh, R. C., Gupta, A. K., Multiple hypergeometric functions related to Lauricella’s functions, Jnanabha 16 (1986), 195–209.

Ernst, T., A Comprehensive Treatment of q-Calculus, Birkhauser, Basel, 2012.

Ernst, T., Convergence aspects for q-Lauricella functions I, Adv. Stud. Contemp.Math. (Kyungshang) 22 (1) (2012), 35–50.

Ernst, T., Convergence aspects for q-Appell functions I, J. Indian Math. Soc., New Ser. 81 (1–2) (2014), 67–77.

Ernst, T., On the complex q-Appell polynomials, Ann. Univ. Mariae Curie-Skłodowska Sect. A 74 (1) (2020), 31–43.

Ernst, T., On confluent q-hypergeometric functions, Appl. Anal. Optim. 4 (3) (2020), 385–404.

Ernst, T., Further results on multiple q-Eulerian integrals for various q-hypergeometric functions, Publ. Inst. Math. (Beograd) (N.S.) 108 (122) (2020), 63–77.

Ernst, T., Three algebraic number systems based on the q-addition with applications, Ann. Univ. Mariae Curie-Skłodowska Sect. A 75 (2) (2021), 45–71.

Exton, H., On certain confluent hypergeometric functions of three variables, Ganita 21 (2) (1970), 79–92.

Exton, H., Certain hypergeometric functions of four variables, Bull. Soc. Math. Grece (N.S.) 13 (1–2) (1972), 104–113.

Karlsson, P., On intermediate Lauricella functions, Jnanabha 16 (1986), 211–222.

Qureshi, M.I, Quraishi,K.A., Khan,B. Arora, A. Transformations associated with quadruple hypergeometric functions of Exton and Srivastava, Asia Pac. J. Math. 4 (1) (2017), 38–48.

Srivastava, H.M., A formal extension of certain generating functions, Glasnik Mat. Ser. III 5 (25) (1970), 229–239.

Srivastava, H.M., A formal extension of certain generating functions II, Glasnik Mat. Ser. III 6 (26) (1971), 35–44.




DOI: http://dx.doi.org/10.17951/a.2023.77.1.13-23
Date of publication: 2023-09-30 21:35:45
Date of submission: 2023-09-26 19:43:20


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