Hash Function Formating Question If a hash function is written:

Hash(Hello||World)


Is that equivalent to Hash(Hello) +  Hash(World) or Hash(HelloWorld) ?

Similarly, is there any difference between Hash(Hello||World) and Hash(Hello,World)?
Typically, the notation || means concatenation, which is to say Hello||World is equivalent to HelloWorld. 

Is that equivalent to Hash(Hello) +  Hash(World) or Hash(HelloWorld)?

So Hash(Hello||World) is equivalent to Hash(HelloWorld).

Is there any difference between Hash(Hello||World) and Hash(Hello,World)?

This depends entirely on what Hello,World is defined to mean.

Notation does not have absolutely defined meaning - what a symbol means in one context can be different from what that symbol means in another context.

The only way to know for sure is to check the definitions of the notation from wherever you found this. 

If there are no such definitions, then it is safe to assume the most common/obvious meaning for the notation. However, if the notation is non-standard, then there may not be a common and obvious meaning for it.