An expansion formula for the multivariable Aleph-function

International Journal of Mathematics Trends and Technology (IJMTT)
© 2016 by IJMTT Journal
Volume-35 Number-2
Year of Publication : 2016
Authors : F.Y Ayant


F.Y. Ayant "An expansion formula for the multivariable Aleph-function", International Journal of Mathematics Trends and Technology (IJMTT). V35(2):111-116 July 2016. ISSN:2231-5373. Published by Seventh Sense Research Group.

The aim of the paper is to establish a general expansion formula for the Aleph-function of several variables. It is significant to observe that a large number of finite and infinite series for this function can be easily summed up by using the summation theorem for ordinary hypergeometric series in the main result. Also, by appropriately specializing the parameters of the multivariable Aleph-function, one can obtain expansion formulas for simpler special functions of one and several variables.

[1] Agrawal M.K and Jain S.S.L. An expansion formula for the I-function of two variables. Vijnana Parishad Anusandhan Patrika 1997, vol 40 (2), page 121-129.
[2] Ayant F.Y. An integral associated with the Aleph-functions of several variables. International Journal of Mathematics Trends and Technology (IJMTT). 2016 Vol 31 (3), page 142-154.
[3] Sharma C.K.and Ahmad S.S.: On the multivariable I-function. Acta ciencia Indica Math , 1994 vol 20,no2, p 113- 116.
[4] C.K. Sharma and P.L. mishra : On the I-function of two variables and its properties. Acta Ciencia Indica Math , 1991 Vol 17 page 667-672.
[5] Sharma K. On the integral representation and applications of the generalized function of two variables , International Journal of Mathematical Engineering and Sciences , Vol 3 , issue1 ( 2014 ) , page1-13.
[6] Slater L.J. Generalized hypergeometric function. Cambridge University Press , Cambridge and London (1966).

Multivariable Aleph-function,Mellin-Barnes contour,generalized hypergeometric function,expansion formula, I-function of several variables, Aleph-function of two variables.