Inequalities involving Mittag-Leffler type $q$-Konhauser polynomial
DOI:
https://doi.org/10.24193/subbmath.2020.3.07Keywords:
$q$-Mittag-Leffler function, $q$-Konhauser Polynomial, Series inequalities, Difference equation, Generating function relation, Series inequality relationsAbstract
In the present work, we propose generalized structure of the $q$-Konhauser polynomial suggested by a generalized $q$-Mittag-Leffler function. For this polynomial, we obtain its difference equation and several other properties involving inequalities are also derived which yield as the particular cases, $q$-analogues of the generating function relations and finite summation formulas.References
R. P. Agarwal, Certain fractional q-integrals and q-derivatives, Proc. Comb. Phil. Soc. 66 (1969), no. 3, 365-370, https://doi.org/10.1017/s0305004100045060.
W. A. Al-Salam, Some fractional q-integarls and q-derivatives, Proc. Edinburgh Math. Soc. 15 (1966), 135-140, https://doi.org/10.1017/s0013091500011469.
W. A. Al-Salam and A. Verma, q-Konhauser polynomials, Pacific Journal of Mathematics 1 (1983), no. 108, 1-7, https://doi.org/10.2140/pjm.1983.108.1.
P. A. Clarkson and F. W. Nijhoff, Symmetries and Integrability of difference equations, Cambridge University press (1999), https://doi.org/10.1017/cbo9780511569432.
B. I. Dave, Extensions of certain inverse series relations and associated polynomials, Ph. D. Thesis, The M. S. University of Baroda, Vadodara (1994).
G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge (1990), https://doi.org/10.1017/cbo9780511526251.004.
W. Hahn, Uber Orthogonal polynome, die q-Differenzengleichungen genugen, Mat. Nachr. 2 (1949), 4-34, https://doi.org/10.1002/mana.19490020103.
B. V. Nathwani, Generalized q-Mittag-Leffler function and its properties, Jour-nal of Divulgaciones Matematicas 18 (2017), no. 1, 10-33.
B. V. Nathwani and B. I. Dave, Fractional q-calculus of anextended q- Mittag-Leffler function, Journal of Fractional Calculus and Applications 9 (2018), no. 1, 64-81, .
J. C. Prajapati, N. Ajudia, and P. Agarwal, Some results due to Konhauser polynomials of first kind and Laguerre polynomials, Applied Mathematics and Computation 247 (2014), 639-650, https://doi.org/10.1016/j.amc.2014.09.020.
E. D. Rainville, Special Functions, Macmillan Co., New York (1960), https://doi.org/10.2307/2309272.
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