As such, Polybius is very aware of the time and place at which the events took place. Polybius journeyed to the site not long after the actual crossing of the Alps, and is more trustworthy than a modern day historian.
The account is a prose form of chronology in that it just tells the story, like a story. It is not interspersed with facts- it is represented as all fact - which is typical of early histories. They did not have many other writers to reference, and the reader most likely wouldn't have been able to access the other books regardless.
The only major discrepancy between Polybius' accounting and that of Livy is that Polybius mentioned they could see Italy from the pass and Livy stated they could not see Italy until they had started the descent.
Titus Livy (59 BCE- 17 CE) is the author of the authorized version of the history of the Roman republic. His writings do betray that he knew little of military matters which would affect the believability of his account of the military operations of Hannibal.2 Again, there is no attempt to evaluate the sources of evidence and it is quite likely that he may have even used Polybius' writings as a possible reference.
As he lived 100 years or so after Hannibal crossed the Alps, this accounting is more subject to inaccuracies due to the passage of time.