[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2020.60.4.731

The p-deformed Generalized Humbert Polynomials and Their Properties

Savalia, Rajesh V. (Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Faculty of Applied Sciences, Charotar University of Science and Technology)
Dave, B.I. (Department of Mathematics, Faculty of Science, The Maharaja Sayajirao University of Baroda)

Publication Information

Kyungpook Mathematical Journal / v.60, no.4, 2020 , pp. 731-752 More about this Journal

Abstract

We introduce the p-deformation of generalized Humbert polynomials. For these polynomials, we derive the differential equation, generating function relations, Fibonacci-type representations, and recurrence relations and state the companion matrix. These properties are illustrated for certain polynomials belonging to p-deformed generalized Humbert polynomials.

Keywords

p-Gamma function; p-Pochhammer symbol; differential equation; generating function relations; mixed relations;

Citations & Related Records

Reference

1	Yu. A. Brychkov, On some properties of the Nuttall function Q_μ,ν(a, b), Integral Transforms Spec. Funct., 25(1)(2014), 33-43.
2	Yu. A. Brychkov and N. V. Savischenko, A special function of communication theory, Integral Transforms Spec. Funct., 26(6)(2015), 470-484. DOI
3	V. V. Bytev, M. Yu. Kalmykov and S.-O. Moch, HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: FD and FS Horn-type hypergeometric functions of three variables, Comput Phys. Commun., 185(2014), 3041-3058. DOI
4	G. B. Costa and L. E. Levine, Nth-order differential equations with finite polynomial solutions, Int. J. Math. Educ. Sci. Tech., 29(6)(1998), 911-914.
5	P. Deligne, P. Etingof, D. S. Freed, L. C. Jeffrey, D. Kazhdan, J. W. Morgan, D. R. Morrison and E. Witten, Quantum fields and strings: a course for mathematicians, American Mathematical Society, 1999.
6	R. Diaz and E. Pariguan, Quantum symmetric functions, Comm. Algebra, 33(6)(2005), 1947-1978. DOI
7	R. Diaz and E. Pariguan, On hypergeometric functions and Pochhammer k-symbol, Divulg. Mat., 15(2)(2007), 179-192.
8	R. Diaz and C. Teruel, q, k-generalized gamma and beta function, J. Nonlinear Math. Phys., 12(1)(2005), 118-134. DOI
9	H. W. Gould, Inverse series relations and other expansions involving Humbert polynomials, Duke Math. J., 32(4)(1965), 697-711. DOI
10	F. B. Hildebrand, Introduction to numerical analysis, Second edition, Dover Publications INC., New York, 1987.
11	P. Humbert, Some extensions of Pincherle's polynomials, Proc. Edinburgh Math. Soc., 39(1)(1920), 21-24. DOI
12	P. Humbert, The confluent hypergeometric functions of two variables, Proc. R. Soc. Edinb., 41(1922), 73-96. DOI
13	B. A. Kniehl and O. V. Tarasov, Finding new relationships between hypergeometric functions by evaluating Feynman integrals, Nuclear Phys. B, 854(3)(2012), 841-852. DOI
14	M. Mignotte and D. Stefanescu, Polynomials: an algorithmic approach, Springer-Verlag, New York, 1999.
15	G. Ozdemir, Y. Simsek, and G. V. Milovanovic, Generating functions for special polynomials and numbers including Apostol-type and Humbert-type polynomials, Mediterr. J. Math., 14(3)(2017), Paper No. 117, 17 pp. DOI
16	G. Polya and G. Szego, Problems and theorems in analysis I, Springer-Verlag, New York-Heidelberg and Berlin, 1972.
17	E. D. Rainville, Special functions, The Macmillan Company, New York, 1960.
18	P. C. Sofotasios , T. A. Tsiftsis, Yu. A. Brychkov, et al., Analytic expressions and bounds for special functions and applications in communication theory, IEEE Trans. Inform. Theory, 60(12)(2014), 7798-7823. DOI
19	E. T. Whittaker and G. N. Watson, A course of modern analysis, 4th ed., Cambridge University Press, Cambridge, 1927.
20	H. M. Srivastava and H. L. Manocha, A treatise on generating functions, Ellis Horwood Limited, John Willey and Sons, 1984.