A production function with variable elasticity of substitution greater than one

The idea of this paper comes from the famous remark of Piketty and Zuckman: "It is natural to imagine that $\sigma$ was much less than one in the eighteenth and nineteenth centuries and became larger than one in the twentieth and twenty-first centuries. One expects a higher elasticity of substitution in high-tech economies where there are lots of alternative uses and forms for capital." The main aim of this paper is to prove the existence of a production function of variable elasticity of substitution with values greater than one.