Euler proves that the infinite product s=(1-x)(1-x^2)(1-x^3)... expands into
the power series s=1-x-x^2+x^5+x^7-..., in which the signs alternate in two's
and the exponents are the pentagonal numbers. Euler uses this to prove his
pentagonal number theorem, a recurrence relation for the sum of divisors of a
positive integer.
%0 Generic
%1 citeulike:3036281
%A Euler, Leonhard
%D 2005
%K Vor1800 available-in-tex-format mathematics number-theory pre1800
%T Demonstration of a theorem about the order observed in the sums of divisors
%U http://arxiv.org/abs/math/0507201
%X Euler proves that the infinite product s=(1-x)(1-x^2)(1-x^3)... expands into
the power series s=1-x-x^2+x^5+x^7-..., in which the signs alternate in two's
and the exponents are the pentagonal numbers. Euler uses this to prove his
pentagonal number theorem, a recurrence relation for the sum of divisors of a
positive integer.
@misc{citeulike:3036281,
abstract = {Euler proves that the infinite product s=(1-x)(1-x^2)(1-x^3)... expands into
the power series s=1-x-x^2+x^5+x^7-..., in which the signs alternate in two's
and the exponents are the pentagonal numbers. Euler uses this to prove his
pentagonal number theorem, a recurrence relation for the sum of divisors of a
positive integer.},
added-at = {2009-08-02T17:14:35.000+0200},
archiveprefix = {arXiv},
author = {Euler, Leonhard},
biburl = {https://www.bibsonomy.org/bibtex/2dac222a67f62c9ba6426422f4c378996/rwst},
citeulike-article-id = {3036281},
citeulike-linkout-0 = {http://arxiv.org/abs/math/0507201},
citeulike-linkout-1 = {http://arxiv.org/pdf/math/0507201},
description = {my bookmarks from citeulike},
eprint = {math/0507201},
interhash = {39e2a6d330e95afec95338563bc66300},
intrahash = {dac222a67f62c9ba6426422f4c378996},
keywords = {Vor1800 available-in-tex-format mathematics number-theory pre1800},
month = Jul,
posted-at = {2008-07-23 08:48:03},
priority = {2},
timestamp = {2009-08-06T10:24:00.000+0200},
title = {Demonstration of a theorem about the order observed in the sums of divisors},
url = {http://arxiv.org/abs/math/0507201},
year = 2005
}