The purpose of the present paper is to introduce a new extension of extended Beta function by product of two Mittag-Leffler functions. Further, we present certain results including summation formulas, integral representations and Mellin transform.

Motivated mainly by a variety of applications of Euler's Beta, hypergeometric, and confluent hypergeometric functions together with their extensions in a wide range of research fields such asengineering, chemical, and physical problems. In this paper, we introduce modified forms of some extended special functions such as Gamma function, Beta function, hypergeometric function and confluent hypergeometric function by making use of the idea given in reference \cite{9}. Also, certain investigations including summation formulas, integral representations and Mellin transform of these modified functions are derived. Further, many known results are obtained asspecial cases of our main results.

The aim of the present paper is to obtain some double and triple generating functions for Laguerre polynomials of two variables. A number of interesting generating functions (known or new) are also derived as special cases of our main results.

The purpose of present paper is to introduce a new extension of Hurwitz-Lerch Zeta function by using the extended Beta function. Some recurrence relations, generating relations and integral representations are derived for that new extension.

Abstract:The aim of this research paper is to derive some hypergeometric formulas of Laguerre polynomials of two, three and several variables. Also we apply this formulas to derive some integral formulas involving Laguerre polynomials of several variables.