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  • This article is about Euler's formula in complex analysis. For Euler's formula in algebraic topology and polyhedral combinatorics see Euler characteristic.Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively, with the argument x given in radians. This complex exponential function is sometimes denoted cis(x) ("cosine plus i sine"). The formula is still valid if x is a complex number, and so some authors refer to the more general complex version as Euler's formula.Euler's formula is ubiquitous in mathematics, physics, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics."
  • In matematica, la formula di Eulero è una formula nel campo dell'analisi complessa che mostra una profonda relazione fra le funzioni trigonometriche e la funzione esponenziale complessa. L'identità di Eulero è un caso particolare della formula di Eulero.La formula di Eulero, dal nome del matematico Leonhard Euler, è stata provata per la prima volta da Roger Cotes nel 1714 e poi riscoperta e resa celebre da Eulero nel 1748. Nessuno dei due vide l'interpretazione geometrica della formula: la visione dei numeri complessi come punti nel piano arrivò solo circa 50 anni dopo, per opera di Caspar Wessel, Argand e Gauss.La dimostrazione più diffusa è basata sullo sviluppo in serie di Taylor della funzione esponenziale.
  • Die eulersche Formel bzw. Eulerformel, in manchen Quellen auch eulersche Relation genannt, ist eine Gleichung, die eine Verbindung zwischen den trigonometrischen Funktionen und den Exponentialfunktionen mittels komplexer Zahlen darstellt.Die eulersche Formel erschien erstmals 1748 in Leonhard Eulers zweibändiger Introductio in analysin infinitorum, zunächst unter der Prämisse, dass der Winkel eine reelle Zahl ist. Diese Einschränkung jedoch erwies sich bald als überflüssig, denn die eulersche Formel gilt gleichermaßen für alle reellen wie komplexen Argumente. Dies ergibt sich aus der reellen eulerschen Formel in Verbindung mit dem Identitätssatz für holomorphe Funktionen.
  • Wzór Eulera – wzór analizy zespolonej wiążący funkcje trygonometryczne z zespoloną funkcją wykładniczą określany nazwiskiem Leonharda Eulera.
  • In integral calculus, complex numbers and Euler's formula may be used to evaluate integrals involving trigonometric functions. Using Euler's formula, any trigonometric function may be written in terms of eix and e−ix, and then integrated. This technique is often simpler and faster than using trigonometric identities or integration by parts, and is sufficiently powerful to integrate any rational expression involving trigonometric functions.
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  • Wzór Eulera – wzór analizy zespolonej wiążący funkcje trygonometryczne z zespoloną funkcją wykładniczą określany nazwiskiem Leonharda Eulera.
  • This article is about Euler's formula in complex analysis. For Euler's formula in algebraic topology and polyhedral combinatorics see Euler characteristic.Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.
  • Die eulersche Formel bzw. Eulerformel, in manchen Quellen auch eulersche Relation genannt, ist eine Gleichung, die eine Verbindung zwischen den trigonometrischen Funktionen und den Exponentialfunktionen mittels komplexer Zahlen darstellt.Die eulersche Formel erschien erstmals 1748 in Leonhard Eulers zweibändiger Introductio in analysin infinitorum, zunächst unter der Prämisse, dass der Winkel eine reelle Zahl ist.
  • In matematica, la formula di Eulero è una formula nel campo dell'analisi complessa che mostra una profonda relazione fra le funzioni trigonometriche e la funzione esponenziale complessa. L'identità di Eulero è un caso particolare della formula di Eulero.La formula di Eulero, dal nome del matematico Leonhard Euler, è stata provata per la prima volta da Roger Cotes nel 1714 e poi riscoperta e resa celebre da Eulero nel 1748.
  • In integral calculus, complex numbers and Euler's formula may be used to evaluate integrals involving trigonometric functions. Using Euler's formula, any trigonometric function may be written in terms of eix and e−ix, and then integrated. This technique is often simpler and faster than using trigonometric identities or integration by parts, and is sufficiently powerful to integrate any rational expression involving trigonometric functions.
rdfs:label
  • Formule d'Euler
  • Euler formülü
  • Euler's formula
  • Euler-képlet
  • Eulerren formula
  • Eulersche Formel
  • Eulerův vzorec
  • Formula di Eulero
  • Formule van Euler
  • Fórmula d'Euler
  • Fórmula de Euler
  • Fórmula de Euler
  • Rumus Euler
  • Wzór Eulera
  • Формула Эйлера
  • Формула на Ойлер
  • オイラーの公式
  • 오일러의 공식
  • Integration using Euler's formula
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