Wikipedia:Reference desk/Archives/Mathematics/2013 June 25

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June 25

Reimann zeta function functional equation.

Does anyone know where I could find a proof that the Reimann zeta function is satisfied by the functional equation? — Preceding unsigned comment added by 109.149.54.175 (talk) 14:52, 25 June 2013 (UTC)

On the Number of Primes Less Than a Given Magnitude gives links to Riemann's original paper, with a proof of exactly that on the first pages. MuDavid (talk) 19:08, 25 June 2013 (UTC) It's Riemann and not Reimann, BTW.

It's also proven in Lars Ahlfors' classic textbook "Complex analysis". This is easier to read than Riemann's proof, and is available in many different languages. Sławomir Biały (talk) 19:18, 25 June 2013 (UTC)

Life Expectancy Probability

I am working on a book of ancient history, dealing with the first-century Near East. I have determined that the overall life expectancy at that time and place was 28 years. But for people who had survived to age 15, the life expectancy was 52 years. One individual I am writing about definitely lived past age 15, but it is unknown how long he lived. My question is this: in this time and place, what is the probability that the individual lived to age 90? If statistics on age distributions, life expectancies, etc. are necessary, it is OK to make assumptions based on current figures for places such as central Africa or Afghanistan. A simple answer would be great, but even better would be a formula into which I could plug figures such as the 52 and 90, and try different scenarios. Thanks very much. 98.169.53.48 (talk) 22:40, 25 June 2013 (UTC)

See [1] for a graph which with a slight adjustment will probably give something close to what you want. Quite a few would reach 75 but very few reach 90. Dmcq (talk) 11:34, 26 June 2013 (UTC)

Excellent reference, thank you. A formula that would take things to 2 decimal places would be more satisfying, but also illusory -- as the attached paper emphasizes, there is only informed approximation to be achieved on ancient demography. 72.209.236.150 (talk) 22:42, 1 July 2013 (UTC)