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2. Multiple integral - Wikipedia

   en.wikipedia.org/wiki/Multiple_integral

   In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in (the real-number plane) are called double integrals, and integrals of a function of three variables over a region ...

3. Rankin–Selberg method - Wikipedia

   en.wikipedia.org/wiki/Rankin–Selberg_method

   Rankin–Selberg method. In mathematics, the Rankin–Selberg method, introduced by (Rankin 1939) and Selberg (1940), also known as the theory of integral representations of L -functions, is a technique for directly constructing and analytically continuing several important examples of automorphic L -functions. Some authors reserve the term for ...

4. Pythagorean triple - Wikipedia

   en.wikipedia.org/wiki/Pythagorean_triple

   A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A triangle whose side lengths are a Pythagorean triple is a right triangle and ...

5. Integration by substitution - Wikipedia

   en.wikipedia.org/wiki/Integration_by_substitution

   Calculus. In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, [1] is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation, and can loosely be thought of as using the chain rule "backwards."

6. Lists of integrals - Wikipedia

   en.wikipedia.org/wiki/Lists_of_integrals

   More detail may be found on the following pages for the lists of integrals: Gradshteyn, Ryzhik, Geronimus, Tseytlin, Jeffrey, Zwillinger, and Moll 's (GR) Table of Integrals, Series, and Products contains a large collection of results. An even larger, multivolume table is the Integrals and Series by Prudnikov, Brychkov, and Marichev (with ...

7. Contour integration - Wikipedia

   en.wikipedia.org/wiki/Contour_integration

   In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane. [1][2][3] Contour integration is closely related to the calculus of residues, [4] a method of complex analysis. One use for contour integrals is the evaluation of integrals along the real line that are ...