# General form of a Transfer Function

A professor is writing the general form of a Transfer Function as:

$$H(s)=k\cdot s^{l}\cdot \frac{\prod\limits_{i=1}^{m}\left(1+\frac{s}{z_{i}}\right)}{\prod\limits_{i=1}^{n}\left(1+\frac{s}{p_{i}}\right)}$$

but in every book and in every source that I have found is never mentioned that way. The poles and zeros are never in fractions in the numerator and denominator. Am I missing something? Has anyone any source to explain the logic behind this specific form of Transfer Function?

1. $$H(s) = K\dfrac{(s-z_1)(s-z_2)\dots(s-z_n)}{(s-p_1)(s-p_2)\dots(s-p_m)}$$
2. $$H(s) = \dfrac{b_ns^n + b_{n-1}s^{n-1}+ \dots + b_0s^0}{a_ms^m + a_{m-1}s^{m-1}+ \dots + a_0s^0}$$