Extended Multivariable Fourth Type Horn Functions

In this paper, we define an extension of multivariable fourth kind Horn functions. Then, we obtainsome generating functions for these functions. Furthermore, we get bilateral generating functionsfor the extended multivariable fourth kind Horn functions and extended first kind Lauricellafunctions. Finally, we derive various families of multilinear and multilateral generating functionsfor these functions and their special cases are also given.

PDF

___

Chaudhry, M. A., Qadir, A., “Srivastava H. M., Paris, R. B., Extended hypergeometric and confluent hypergeometric functions”, Appl. Math. Comput., 159:589-602, (2004).
Chaudhry, M. A., Zubair, S. M., “Generalized incomplete gamma functions with applications”, J. Comput. Appl. Math., 55:99-124, (1994).
Chaudhry, M. A., Qadir, A., Rafique, M., Zubair, S. M., “Extension of Euler's beta function”, J. Comput. Appl. Math., 78:19-32, (1997).
Srivastava, H. M, Parmar R. K. and Chopra P., “A class of extended fractional derivative operators and associated generating relations involving hypergeometric functions”, Axioms, 1:238-258, (2012).
L. Minjie, “A class of extended hypergeometric functions and its applications,” arXiv: 1302.2307 [math.CA], (2013).
Erkuş, E. and Srivastava, H.M., “A unified presentation of some families of multivariable polynomials”, Integral Transform. Spec. Funct., 17: 267-273, (2006).
Aktas, R. and Erkuş-Duman. E., “The Laguerre polynomials in several variables”, Math. Slovaca, 63:(3), 531-544, (2013).
Atash, A. A. and Obad, A. M., “Bilateral generating functions for the generalized Horn's function ( ) ( ) 4k n H ”, International Journal of Mathematical Analysis, 8:2861-2867, (2014).
Horn, J., “Hypergeometrische Funktionen zweier Veränderlichen”, Math. Ann., 105:381-407, (1931).
Srivastava, H. M. and Manocha, H. L. “A Treatise on Generating Functions”, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, 1984.
Exton H., “Multiple hypergeometric functions and applications”, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, (1976).
Altın A, Erkuş E, Tasdelen F., “The q-Lagrange polynomials in several variables”, Taiwanese J.Math., 10:1131-1137, (2006).
Kızılateş C, Çekim B., “New families of generating functions for q-Fibonacci and related to polynomials”, Ars Combinatoria, 136:397-404, (2018).
Erkuş-Duman E, Tuglu N., “Generating functions for the generalized bivariate Fibonacci and Lucas polynomials”, J. Comput. Anal.Appl., 5:815-821, (2015).
Korkmaz-Duzgun D. and Erkuş-Duman E., “The Laguerre Type d-Orthogonal Polynomials”, Journal of Science and Arts, 1(42), 95-106, (2018).