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2. Euler's identity - Wikipedia

   en.wikipedia.org/wiki/Euler's_identity

   In mathematics, Euler's identity[note 1] (also known as Euler's equation) is the equality where. is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula when evaluated for .

3. Euler's formula - Wikipedia

   en.wikipedia.org/wiki/Euler's_formula

   v. t. e. 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, one has where e is the base of the natural logarithm, i is the imaginary ...

4. Integration by parts - Wikipedia

   en.wikipedia.org/wiki/Integration_by_parts

   Integration by parts. In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative.

5. List of formulas in Riemannian geometry - Wikipedia

   en.wikipedia.org/wiki/List_of_formulas_in...

   The gradient of a function is obtained by raising the index of the differential , whose components are given by: =; =; =, = = The divergence of a vector field with components is

6. Euler–Maclaurin formula - Wikipedia

   en.wikipedia.org/wiki/Euler–Maclaurin_formula

   The Euler–Maclaurin formula provides expressions for the difference between the sum and the integral in terms of the higher derivatives f(k)(x) evaluated at the endpoints of the interval, that is to say x = m and x = n. Explicitly, for p a positive integer and a function f(x) that is p times continuously differentiable on the interval [m,n ...

7. Euler's continued fraction formula - Wikipedia

   en.wikipedia.org/wiki/Euler's_continued_fraction...

   Euler derived the formula as connecting a finite sum of products with a finite continued fraction. (+ (+ (+))) = + + + + = + + + +The identity is easily established by induction on n, and is therefore applicable in the limit: if the expression on the left is extended to represent a convergent infinite series, the expression on the right can also be extended to represent a convergent infinite ...