We investigate evolution of properties of an extended s-wave superconductor, when the order parameter varies from an s-wave to a g-wave continuously, by using a model order parameter ∆(k) = ∆0((1−x)+x sin 4 θ cos 4φ). The evolution of the gap amplitude, the density of states, and the specific heat are mainly focused on. For x < 0.5, due to the existence of a finite sized gap, the characteristic behaviors more or less follow those of the s-wave. Sudden changes in the characteristic behaviors come out for x ≥ 0.5, due to appearances of nodes. For x = 0.5, point nodes in the order parameter on the Fermi surface appear, while for x > 0.5, line nodes appear. Although they are different kinds of nodes which would usually induce different power-law dependencies in superconducting properties, interestingly enough, they give rise to the same characteristic behavior. The detailed structure of the point nodes for x = 0.5 is investigated, and it is explained why they lead to the same dependence as the line nodes.

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