Lower incomplete gamma function

Question

From Wikipedia,

The upper incomplete gamma function defined as:

$$\Gamma(s,x) = \int_{x}^{\infty}t^{s-1}e^{-t}dt$$

whereas the lower incomplete gamma function is defined as

$$\gamma(s,x) = \int_{0}^{x}t^{s-1}e^{-t}dt.$$

My question is that can we write the following equation. How can we write or is there any reference

$$\gamma(s + 1,x) = \int_{0}^{x}t^{s}e^{-t}dt.$$

Thanks in advance: