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The authors have established some differential formulae for the -function of two variables . The integrand of the main integral evaluated in this chapter consists of product of the -function of two variables and a class of double Barnes integral. The evaluation of four integrals of -function of two variables proposed by Singh and Mandia (2013) and their applications in deriving double half-range Fourier series for the -function of two variables. A multiple integral and a multiple half-range Fourier series of the -function of two variables are derived analogous to the double integral and double half-range Fourier series of the -function of two variables. We have evaluated an integral involving an exponential function, Sine function, generalized hypergeometric series and -function of two variables. We have introduced an even function on the interval and investigate an integral formula to evaluate the Fourier cosine series involving products of general class of multivariable polynomials (1987) and multivariable -functions due to Gautam (1986).