Received 1 February 2016; accepted 27 March 2016; published 30 March 2016
The Lauricella’s function is defined and represented as follows 
where denotes the Pochhammer’s symbol defined by
Also, we note that
The generalized Lauricella’s function of several variables is defined as follows 
the coefficients for all
are real and positive; abbreviates the array of A parameters; abbreviate
the array of parameters for all with similar inter pretations for and . Note that, when the coefficients in Equation (1.8) equal to 1, the generalized Lauricella function (1.8) reduces to the following multivariable extension of the Kamp’e de F’eriet function  :
In the theory of hypergeometric series, classical summation theorems such as Dixon, Watson and Whipple for the series, have many generalizations and wide applications; see for example   -  . In the present investigation, we shall require the following generalization of the classical Dixon’s theorem for the series  :
where denotes the greatest integer less than or equal to x and denotes the usual absolute value of x. The coefficients are given respectively in  . When, (1.12) reduces immediately to the classical Dixon's theorem  , (see also  )
2. Extension Formulas
In this section, the following two extension formulas for Lauricella’s function of the second kind of several variables will be established:
The coefficients and can be obtained from the tables of and given in  by replacing a by and respectively.
Proof of (2.1): Denoting the left hand side of (2.1) by S, expanding in a power series and using the results  :
Separating (2.9) into its even and odd terms, we have
Finally, in (2.11) if we use the result (1.12), then we obtain the right hand side of (2.1). This completes the proof of (2.1). The result (2.2) can be proved by the similar manner.
3. Special Cases
1) In (2.1), if we take and use the results (1.3)-(1.7), then after some simplification we obtain the following transformation formula:
which for, reduces immediately to a known result of Bailey 
where is Appell’s function  .
2) Similarly, in (2.2) if we take and use the results (1.3)-(1.7), then we obtain the following transformation formula:
3) In (2.2) if we take, then we get a known extension formulas  for Lauricella’s function of three va-
 Lavoie, J.L., Grondin, F. and Rathie, A.K. (1996) Generalizations of Whipple’s Theorem on the Sum of a . Journal of Computational and Applied Mathematics, 72, 293-300.