Consider the following circuit with Vs=1V, R=1Ω and C=1F. The voltage transfer function of the resistor can be written as Vr(s)/Vs(s)=s/(s+1). Now I understand s is complex frequency and at s=∞ the transfer function becomes unity since capacitor acts as a short and Vs=Vr. What I don't understand is at s=-1, the TF becomes infinity. If s=-1 and s=σ+jω, σ=-1 gives TF=∞. What is the meaning of this? What is the general significance of σ? I know jω represents the oscillations in the system but what does the real part σ represent?