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For the multiple zeta function zeta2(s1,s2) of two variables,we obtain itsintegral representation(involving product of Hurwitz zeta functions) over theinterval [1,infinity),with respect to second variable of Hurwitz zeta functionand also obtain a good approximate to it as a function of s1 and s2,for s1>=1and s2>1.In particular this approximate is explicitly computable,when s1,s2differ by an even integer and is good,when s2 is large.We treat zeta3(s1,s2,s3)likewise.

Zeta2(s1,s2),Zeta3(s1,s2,s3):Integral Expressions and Approximates