The extended Srivastavas triple hypergeometric functions and their integral representations

Volume 9, Issue 6, pp 4860--4866 http://dx.doi.org/10.22436/jnsa.009.06.121

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1746 Downloads
• 2819 Views

Authors

Ayşegül Çetinkaya - Dept. of Mathematics, Ahi Evran Univ., 40100 Kırsehir, Turkey. M. Baki Yağbasan - Dept. of Mathematics, Ahi Evran Univ., 40100 Kırsehir, Turkey. İ. Onur Kıymaz - Dept. of Mathematics, Ahi Evran Univ., 40100 Kırsehir, Turkey.

Abstract

We introduce the extended Srivastava's triple hypergeometric functions by using an extension of beta function. Furthermore, some integral representations are given for these new functions.

Share and Cite

Keywords

• Beta function
• Srivastava's triple hypergeometric functions
• Appell's hypergeometric function
• Exton's function.

MSC

•  33C70
•  33C05
•  33C60

References

• [1] M. Bozer, M. A. Özarslan, Notes on generalized gamma, beta and hypergeometric functions, J. Comput. Anal. Appl., 15 (2013), 1194--1201


• [2] M. A. Chaudhry, A. Qadir, M. Rafique, S. M. Zubair, Extension of Euler's beta function, J. Comput. Appl. Math., 78 (1997), 19--23


• [3] M. A. Chaudhry, A. Qadir, H. M. Srivastava, R. B. Paris, Extended hypergeometric and con uent hypergeometric functions, Appl. Math. Comput., 159 (2004), 589--602


• [4] J. Choi, A. Hasanov, H. M. Srivastava, M. Turaev, Integral representations for Srivastava's triple hypergeometric functions, Taiwanese J. Math., 15 (2011), 2751--2762


• [5] J. Choi, A. Hasanov, M. Turaev, Integral representations for Srivastava's hypergeometric function \(H_A\), Honam Math. J., 34 (2012), 113--124


• [6] J. Choi, A. Hasanov, M. Turaev, Integral representations for Srivastava's hypergeometric function \(H_B\), J. Korean Soc. Math. Educ. Ser. B, Pure Appl. Math., 19 (2012), 137--145


• [7] J. Choi, A. Hasanov, M. Turaev, Integral representations for Srivastava's hypergeometric function \(H_C\), Honam Math. J., 34 (2012), 473--482


• [8] A. Hasanov, H. M. Srivastava, M. Turaev, Decomposition formulas for some triple hypergeometric functions, J. Math. Anal. Appl., 324 (2006), 955--969


• [9] M. J. Luo, G. V. Milovanovic, P. Agarwal, Some results on the extended beta and extended hypergeometric functions, Appl. Math. Comput., 248 (2014), 631--651


• [10] M. J. Luo, R. K. Raina, Extended generalized hypergeometric functions and their applications, Bull. Math. Anal. Appl., 5 (2013), 65--77


• [11] M. A. Özarslan, Some remarks on extended hypergeometric, extended con uent hypergeometric and extended Appell's functions, J. Comput. Anal. Appl., 14 (2012), 1148--1153


• [12] M. A. Özarslan, E. Özergin, Some generating relations for extended hypergeometric functions via generalized fractional derivative operator, Math. Comput. Modelling, 52 (2010), 1825--1833


• [13] E. Özergin, M. A. Özarslan, A. Altın, Extension of gamma, beta and hypergeometric functions, J. Comput. Appl. Math., 235 (2011), 4601--4610


• [14] E. D. Rainville, Special functions, Reprint of 1960 first edition, Chelsea Publishing Co., Bronx, New York (1971)


• [15] H. M. Srivastava, Hypergeometric functions of three variables, Ganita, 15 (1964), 97--108


• [16] H. M. Srivastava, Some integrals representing triple hypergeometric functions, Rend. Circ. Mat. Palermo, 16 (1967), 99--115


• [17] H. M. Srivastava, P. Agarwal, S. Jain, Generating functions for the generalized Gauss hypergeometric functions, Appl. Math. Comput., 247 (2014), 348--352


• [18] H. M. Srivastava, P. W. Karlsson, Multiple Gaussian hypergeometric series, Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley and Sons, Inc.], New York (1985)


• [19] H. M. Srivastava, R. K. Parmar, P. Chopra, A class of extended fractional derivative operators and associated generating relations involving hypergeometric functions,, Axioms, 1 (2012), 238--258