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For the Tornheim double zeta function T(s1,s2,s3) of complex variables,weobtain its functional equations,which are new.Using the calculus of r-th orderderivative of zeta(s,alpha) as a function of alpha(developed in author[7])asthe tool,we obtain with ease an expression for T(s,s,s) for any complex s;andevaluate T(n,n,n) for any integer n>=1;and also evaluate T(n1,0,n2)for integersn1,n2>1 with n1+n2 odd.We obtain for Tornheim zeta function,the counterparts ofEuler's formula for zeta(2n)and its analogue for zeta(2n+1),where Zeta(s) isRiemann zeta function.

Functional Equations of Tornheim Zeta Function and the alpha-calculus of r-th order derivative of Zeta(s,alpha)