Rationale of the SHA-256 sigma function definitions

When the sigma functions are defined in equations (4.4) and (4.5) in FIPS PUB 180-4, the defined functions show the traditional sigma summation symbol, with limits 0 to {256} and 1 to {256}. The definitions, however, are in terms of circular right shift and XOR operations. Why is a summation symbol used here?

• I'm reading the {256} as meaning for SHA-256 (and derivatives). – fgrieu Sep 22 '19 at 8:41

It is the naming of functions and the functions are already defined - rotations (ROTR) and x-ors ($$\oplus$$). There are two $$\Sigma$$ and $$\sigma$$ functions for SHA-256 and SHA-512 series. And, in Greek, the $$\Sigma$$ is capital of $$\sigma$$.
The upper index represents the SHA family as 256 and 512. The sub-index, selects the function. $$\Sigma_{0}^{\{256\}}$$ means the first $$\Sigma$$ function of SHA-256 series. Note the curly braces.