## E368 -- De curva hypergeometrica hac aequatione expressa $$y = 1. 2. 3. \ldots x.$$

(On a hyperbolic curve expressed by this equation $$y = 1. 2. 3. \ldots x.$$)

Summary:

Euler discusses $$G(x)$$ some more, though he denotes it $$P(x)$$, along with $$P'(x)$$, at $$x = 1/2, 3/2$$ and $$5/2$$.

According to the records, it was presented to the St. Petersburg Academy on December 19, 1765.

Publication:
• Originally published in Novi Commentarii academiae scientiarum Petropolitanae 13, 1769, pp. 3-66
• Opera Omnia: Series 1, Volume 28, pp. 41 - 98
Documents Available:
• Original publication: E368

• The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E368 include:
• Dutka J., “The early history of the factorial function.” Archive for History of Exact Sciences, 43 (3), pp. 225-249 (1991).
• Ferraro G., “Some aspects of Euler's theory of series: Inexplicable functions and the Euler-Maclaurin summation formula.” Historia Mathematica, 25 (3), pp. 290-317 (Aug 1998).
• Gould HW., “Euler formula for nth differences of powers.” American Mathematical Monthly, 85 (6), pp. 450-467 (1978).