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Yes; and there are a number of sites out there on how to analyze the lottery,
this being one of them.
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That site makes the derivation far too complicated. You don't need to use the Poisson distribution and then sum an infinite series as that site does. You can calculate your expected share of the jackpot by computing the expected jackpot money paid out divided by the number of tickets sold.
The expected total jackpot money paid out is the jackpot times the probability at least one person wins. This is easy to compute if you assume the tickets are independent.
If you have one of N tickets which win independently with probability p, your expected share of the jackpot J is J*(1-(1-p)^N)/N.