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Euler's formula — This article is about Euler s formula in complex analysis. For Euler s formula in algebraic topology and polyhedral combinatorics see Euler characteristic. Part of a series of articles on The mathematical constant e … Wikipedia
Euler–Maclaurin formula — In mathematics, the Euler–Maclaurin formula provides a powerful connection between integrals (see calculus) and sums. It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using… … Wikipedia
Euler's formula — 1. Math. the theorem that ei x = cos(x) + i sin(x). 2. Mech. a formula for determining the maximum load that can be applied to a given column without causing it to buckle. [1945 50; named after L. EULER] * * * Either of two important mathematical … Universalium
euler's formula — noun Usage: usually capitalized E : a general engineering formula relating to the strength of a long strut and obtained by mathematical analysis assuming the strut to be initially very slightly bent and neglecting the (dy/dx)² term in the… … Useful english dictionary
Proof of the Euler product formula for the Riemann zeta function — We will prove that the following formula holds::egin{align} zeta(s) = 1+frac{1}{2^s}+frac{1}{3^s}+frac{1}{4^s}+frac{1}{5^s}+ cdots = prod {p} frac{1}{1 p^{ s end{align}where zeta; denotes the Riemann zeta function and the product extends over… … Wikipedia
Fórmula de Euler-Maclaurin — En matemáticas, la fórmula de Euler Maclaurin relaciona a integrales con series. Esta fórmula puede ser usada para aproximar integrales por sumas finitas o, de forma inversa, para evaluar series (finitas o infnitas) resolviendo integrales. La… … Wikipedia Español
Fórmula de Euler — La fórmula o relación de Euler, atribuida a Leonhard Euler, establece que: para todo número real x. Aquí, e es la base del logaritmo natural, i es la unidad imaginaria, sin x y cos x son funciones trigonométricas. O bien: siendo z la… … Wikipedia Español
Euler's identity — [ 300px|thumb|right|The exponential function e z can be defined as the limit of nowrap|(1 + z / N ) N , as N approaches infinity, and thus e iπ is the limit of nowrap|(1 + iπ/N ) N . In this animation N takes various increasing values from 1 to… … Wikipedia
Euler's continued fraction formula — In the analytic theory of continued fractions, Euler s continued fraction formula is an identity connecting a certain very general infinite series with an infinite continued fraction. First published in 1748, it was at first regarded as a simple… … Wikipedia
Euler characteristic — In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic is a topological invariant, a number that describes one aspect of a topological space s shape or structure. It is commonly denoted… … Wikipedia
