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Abstract
The objective of this paper is to establish the q-recurrence relations, q-difference equations for basic analogue of Fox's H-function and then obtain the canonical equation associated with each family of multivariable q-analogue of Fox's H-function and generating functions of families of basic analogue of Fox's H-function. A significantly large number of works on the subject of H- function gives interesting account of the theory and its applications in many different areas of mathematical analysis. A lot of research work has been recently come up on the study and development of a function that is more general.Â
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How to Cite
Sharma, R., & Dwivedi, P. (2014). Symmetry Techniques and Generating Functions for Basic Analogue of Fox’s H-Function. International Journal of Emerging Trends in Science and Technology, 1(09). Retrieved from https://igmpublication.org/ijetst.in/index.php/ijetst/article/view/421
References
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4. Mathai, A.M. and Saxena, R.K. (1978). The H-Function with Application in Statistics and Other Disciplines, John Wiley and Sons, Inc., New York.
5. Miller, W. (1968). Lie theory and Special Functions, Academic Press, New York.
6. Miller, W. (1970). Lie theory and q-difference equations, SIAM J. Math.
7. Anal. 1, 171-188.
8. Purohit, S.D., Yadav, R.K. and Kalla, S.L. (2008). Certain expansion fourmulae involving a basic analogue of Fox's H-functions, Applications and Applied Mathematics, 3(1), 128-136.
9. Saxena, R.K. and Rajendra Kumar (1995). A basic analogue of the generalized H-function, Le Matematiche, L-Fascicolo II, 263-271.
10. Saxena, R.K., Modi, G.C. and Kalla, S.L. (1983). A basic analogue of Fox's H-function, Rev. Tec. Ing. Univ., Zulia, 6, 139-143.
11. Saxena, R.K., Yadav, R.K., Purohit, S.D. and Kalla, S.L. (2005). Kaber fractional q-integral operator of the basic analogue of the H-function, Rev. Tec. Ing. Univ. Zulia, 28(2), 154 - 158.
12. Yadav, R.K. and Purohit, S.D. (2006). On fractional q-derivatives and transformations of the generalized basic hypergeometric functions, J. Indian Acad. Math, 28(2), 321 – 326.
2. Kalnins, E.G. and Miller, W. (1989). Symmetry techniques for q-series; Askey-Wilson polynomials, Rocky Mtn. J. Math.
3. Mathai, A.M. and Saxena, R.K. (1973). Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Springer-Verlag, Berlin.
4. Mathai, A.M. and Saxena, R.K. (1978). The H-Function with Application in Statistics and Other Disciplines, John Wiley and Sons, Inc., New York.
5. Miller, W. (1968). Lie theory and Special Functions, Academic Press, New York.
6. Miller, W. (1970). Lie theory and q-difference equations, SIAM J. Math.
7. Anal. 1, 171-188.
8. Purohit, S.D., Yadav, R.K. and Kalla, S.L. (2008). Certain expansion fourmulae involving a basic analogue of Fox's H-functions, Applications and Applied Mathematics, 3(1), 128-136.
9. Saxena, R.K. and Rajendra Kumar (1995). A basic analogue of the generalized H-function, Le Matematiche, L-Fascicolo II, 263-271.
10. Saxena, R.K., Modi, G.C. and Kalla, S.L. (1983). A basic analogue of Fox's H-function, Rev. Tec. Ing. Univ., Zulia, 6, 139-143.
11. Saxena, R.K., Yadav, R.K., Purohit, S.D. and Kalla, S.L. (2005). Kaber fractional q-integral operator of the basic analogue of the H-function, Rev. Tec. Ing. Univ. Zulia, 28(2), 154 - 158.
12. Yadav, R.K. and Purohit, S.D. (2006). On fractional q-derivatives and transformations of the generalized basic hypergeometric functions, J. Indian Acad. Math, 28(2), 321 – 326.