E541 -- Evolutio producti infiniti \((1-x)(1-xx)(1-x^3)(1-x^4)(1-x^5)\) [etc.] in seriem simplicem
(The expansion of the infinite product \((1-x)(1-xx)(1-x^3)(1-x^4)(1-x^5)\) [etc.] into a single series)
(based on Jordan Bell's abstract)
This paper does exactly what the title says it does. It expands the given series to arrive at the familiar "pentagonal number" expansion, also known
as the pentagonal number theorem, and recalls its application to partition numbers.
According to the records, it was presented to the St. Petersburg Academy on August 14, 1775.
p. 47 is missing the word “etc.”
Originally published in Acta Academiae Scientarum Imperialis Petropolitinae 1780, 1783, pp. 47-55
Opera Omnia: Series 1, Volume 3, pp. 472 - 479
- Original Publication: E541
- English translation (Jordan Bell): E541
- German translation (Artur Diener and Alexander Aycock): E541
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