\[s_{2}(a,x)\sim-\frac{c_{2}}{1!2x^{2}}-\frac{d_{4}}{2!2^{2}x^{4}}+\frac{c_{6}}{%
3!2^{3}x^{6}}+\frac{d_{8}}{4!2^{4}x^{8}}-\cdots.\]