Analysing circuit for digital filter design
You could express the impedances of the components in terms of s, i.e. sL, 1/sC, R. This should allow you to determine the transfer function H(s). This, I reckon, will give you a zero at the origin and two poles on the left half of the s-plane. Once you have a transfer function in terms of s, you can transform this to the z-plane. One method is the bilinear transform. Substituting for s will lead to an H(z). H(z) can be realised as an IIR filter.