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I read somewhere that there is an ancient tablet which has an entry on the very day of Alex's death. Is it reliable information?s

A contemporary Babylonian
account of the death of
Alexander the Great
On the last day of the month Aiaru in the fourteenth year of his reign, Alexander died in Babylon. The only contemporary source describing the event is the so-called Astronomical diary, a day-by-day account of celestial phenomena, written by the officials of the Esagila temple complex. The diary mentions other events as well, e.g., the level of the Euphrates, the weather, the food prices, incidents concerning Babylon and its temples, and political events - after all, the celestial phenomena were omens of important political changes.
The following is the Diary of the second month, Aiaru, of 323 BCE. Unfortunately, the death of Alexander occurred in a clouded week; there are almost no observations. Because the tablet, which is now in the British Museum, is a bit damaged, entire days are missing.


[Year fourteen of Alexander, Month Two]
[The first part is missing.] Night of the fourteenth, beginning of the night, the moon was [lacuna] in front of Theta Ophiuchi.[1] [Night of the eighteenth,] first part of the night, Mercury was fourteen fingers above Saturn. [lacuna] crossed the sky. The twenty-first: clouds crossed the sky. Night of the twenty-second: clouds [crossed the sky; lacuna] [Night of the twenty-third: lacuna] 2 2/3 cubits; clouds were in the sky. The twenty-fourth: clouds [were in the sky]. [lacuna] clouds crossed the sky. Night of the twenty-seventh: clouds crossed the sky. The twenty-seventh: [lacuna] [The night of the twenty-eighth?; lacuna] stood to the east. The twenty-ninth: The king died. Clouds [were in the sky].[2] [That month, the equivalent for 1 shekel of silver was: lacuna; 3] cress, 1 s++t 4 qa; sesame 3 1/2 qa. [At that time; lacuna] Saturn was in Gemini, at the end of the month in Cancer; Mars was in Virgo. [lacuna] the Gate of B+¬l [lacuna] [4]


Note 1:
This observation can be dated on May 26, 323 BCE.
Note 2:
The twenty-ninth of Aiaru is the period between the evening of June 10 and the evening of June 11, 323 BCE. We can, however, be more precise. There are two kinds of entries in the Astronomical diary: some are introduced with words like 'Night of the twenty-seventh', others with 'The twenty-seventh'. In the first case, the entry starts with observations made in the night (and may or may not continue with the observations made during the day), in the se

It is possible to be even more precise. According to the Life of Alexander by the Greek author Plutarch (section 76.9), the Macedonian Royal Diaries reported Alexander's death pros deil+¬n. Although deil+¬ is sometimes translated as 'evening', it is in fact an indication of the ninth and tenth hours of the day - that is, in the week of the summer solstice, between three and six o' clock. There is one other possibility. That is that Alexander died on June 10 before six o' clock, and that the astronomer heard the news after dawn on June 11. In view of the fact that the man had to stay awake all night, and was working in the religious center of the city, where prayers for the dead king had to be said, the author of this web-article supposes that this is less likely, although it can not be excluded completely. Note 3:
At the end of the month, the author of the Astronomical diary sums up the prices of important commodities. Note 4:
The Gate of B+¬l was situated in the east. The Greek author Arrian of Nicomedia tells us that the Babylonian astrologers (which he calls Chaldaeans) advised Alexander not to enter the city through this gate (click here). The Astronomical diary seems to have contained a reference to this incident.


Literature
Paul Bernard, 'Nouvelle contribution de l' +¬pigraphie cun+¬iforme +á l' histoire hell+¬nistique' in: Bulletin de correspondance Hell+¬nique 114 (1990) pages 514-541
Leo Depuydt, 'The Time of Death of Alexander the Great: 11 June 323 BC, ca. 4:00-5:00 PM' in: Die Welt des Orients 28 (1997) 117-135
Abraham Sachs and Hermann Hunger, Astronomical diaries and related texts from Babylon, volume I, 1988 Vienna This is from a website.