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Leonhard Euler proved the Euler product formula for the Riemann zeta function in his thesis Variae observationes circa series infinitas (Various Observations about Infinite Series), published by St Petersburg Academy in 1737. [1] [2]
This was proved by Leonhard Euler in 1737, [1] and strengthens Euclid's 3rd-century-BC result that there are infinitely many prime numbers and Nicole Oresme's 14th-century proof of the divergence of the sum of the reciprocals of the integers (harmonic series).
This is a topic category for the topic Leonhard Euler. Pages in category "Leonhard Euler" The following 44 pages are in this category, out of 44 total. This list ...
Leonhard Euler investigated them and associated polynomials in his 1755 book Institutiones calculi differentialis. The polynomials presently known as Eulerian polynomials in Euler's work from 1755, Institutiones calculi differentialis, part 2, p. 485/6. The coefficients of these polynomials are known as Eulerian numbers.
In number theory, an Euler product is an expansion of a Dirichlet series into an infinite product indexed by prime numbers. The original such product was given for the sum of all positive integers raised to a certain power as proven by Leonhard Euler .
Euler's Disk, invented between 1987 and 1990 by Joseph Bendik, [1] is a trademarked scientific educational toy. [2] It is used to illustrate and study the dynamic system of a spinning and rolling disk on a flat or curved surface. It has been the subject of several scientific papers. [3] Bendik named the toy after mathematician Leonhard Euler. [4]
Euler is regarded as arguably the most prolific contributor in the history of mathematics and science, and the greatest mathematician of the 18th century. [12] [11] His 866 publications and his correspondence are being collected in the Opera Omnia Leonhard Euler which, when completed, will consist of 81 quartos.
The Euler function may be expressed as a q-Pochhammer symbol: = (;). The logarithm of the Euler function is the sum of the logarithms in the product expression, each of which may be expanded about q = 0, yielding