Of course, in \eqref{*} $\phi$ denotes the [[Euler function|Euler function]].
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...|coprime]] $(k + 1)$-tuple together with $n$. This is a generalisation of Euler's [[totient function]], which is $J_1$.
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of the Euler $ \phi $-function (cf. [[Euler function|Euler function]]).
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L. Euler [[#References|[1]]] was the first to study Bernoulli polynomials for arbitr
and are closely connected with the [[Euler polynomials|Euler polynomials]]
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A collection of solutions of the [[Euler equation|Euler equation]], depending on $n$ arbitrary constants and filling without mutual
depends. Euler's equation is understood in the vector sense, that is, it is a system of $n
2 KB (411 words) - 16:38, 24 November 2018
...of Venn diagrams goes back to L. Euler and they are sometimes also called Euler diagrams.
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...Irregularity|irregularity]] $q=5$, with topological [[Euler characteristic|Euler characteristic]] (in case $k=\mathbf C$) equal to 27. From the Fano surface
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...mal [[Euler identity]] beween the Dirichlet series $L(a,s)$ and a formal [[Euler product]] over primes
and is [[Totally multiplicative function|totally multiplicative]] if the Euler product is of the form
2 KB (358 words) - 17:25, 11 November 2023
...ence $x^3\equiv a$ ($\bmod\,p$) may be checked for solvability using the [[Euler criterion]]: The congruence $x^3\equiv a$ ($\bmod\,p$), $(a,p)=1$, is solva
...the form $p=x^2+27y^2$ with integers $x$ and $y$ (a result conjectured by Euler and first proved by Gauss).
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...[[Polyhedron, abstract|Polyhedron, abstract]]) with [[Euler characteristic|Euler characteristic]] equal to 2 can be realized as a convex polyhedron. Here, a
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...elative to another one $0x'y'z'$ with the same origin and orientation. The Euler angles are regarded as the angles through which the former must be successi
These angles were introduced by L. Euler (1748).
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...ans of the series (2), which converges throughout the complex plane, or by Euler's formula
For Euler's formula see also [[Euler formulas|Euler formulas]].
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...o construct the formulas of an iteration method. Thus, after e.g. applying
Euler's method, (12) is replaced by the relations
Numerical integration of (15) by
Euler's method with respect to the points <img align="absmiddle" border="0" src="
15 KB (2,038 words) - 17:21, 7 February 2011
''Euler circle, Feuerbach circle''
...nine-point circle. The points $H,T,O,E$ then lie on a straight line (the [[Euler line]]), $E$ being the midpoint of the segment $HO$, and the pair of points
2 KB (345 words) - 19:10, 6 November 2016
...come in pairs. Two important early results were the minmax theorem and the Euler equation.
==Euler equation.==
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A non-orientable surface with [[Euler characteristic]] zero whose boundary is a closed curve. The Möbius strip c
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...$\phi(2|d|)/2$ or $\phi(4|d|)/2$, where $\phi(n)$ is the [[Euler function|Euler function]]. The quadratic reciprocity law makes it possible to establish fa
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...bra was first given by J. d'Alembert in 1746. There followed the proofs of Euler, P.S. Laplace, J.L. Lagrange and others in the second half of the 18th cent
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is Euler's [[beta-function]]
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is the [[Euler characteristic|Euler characteristic]] of $ V $.
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