• In complex analysis, a partial fraction expansion is a way of writing a meromorphic function f ( z ) {\displaystyle f(z)} as an infinite sum of rational...
    10 KB (2,604 words) - 20:46, 11 April 2023
  • Thumbnail for Residue (complex analysis)
    contour integration Morera's theorem Partial fractions in complex analysis Ahlfors, Lars (1979). Complex Analysis. McGraw Hill. Marsden, Jerrold E.; Hoffman...
    15 KB (3,101 words) - 12:03, 13 December 2024
  • continued fractions that are rapidly convergent almost everywhere in the complex plane. The long continued fraction expression displayed in the introduction...
    51 KB (8,708 words) - 00:22, 21 July 2025
  • Thumbnail for Holomorphic function
    That all holomorphic functions are complex analytic functions, and vice versa, is a major theorem in complex analysis. Holomorphic functions are also sometimes...
    25 KB (3,490 words) - 21:26, 15 June 2025
  • unlike the Fourier transform, when regarded in this way as an analytic function, the techniques of complex analysis, and especially contour integrals, can...
    76 KB (9,706 words) - 20:20, 25 July 2025
  • Thumbnail for Fraction
    rational fractions with integer coefficients. The term partial fraction is used when decomposing rational fractions into sums of simpler fractions. For example...
    67 KB (9,636 words) - 01:44, 23 April 2025
  • In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane. Contour...
    47 KB (9,989 words) - 18:42, 12 July 2025
  • glossary of concepts and results in real analysis and complex analysis in mathematics. In particular, it includes those in measure theory (as there is no...
    28 KB (4,377 words) - 01:08, 19 July 2025
  • In complex analysis, Gauss's continued fraction is a particular class of continued fractions derived from hypergeometric functions. It was one of the first...
    16 KB (4,207 words) - 07:06, 27 April 2025
  • Rational function (category All Wikipedia articles written in American English)
    over complex numbers. Partial fraction decomposition Partial fractions in integration Function field of an algebraic variety Algebraic fractions – a generalization...
    17 KB (2,416 words) - 04:18, 24 June 2025
  • Differentiation under the integral sign Trigonometric substitution Partial fractions in integration Quadratic integral Proof that 22/7 exceeds π Trapezium...
    4 KB (389 words) - 12:14, 10 February 2024
  • Thumbnail for Taylor series
    Taylor series (category Complex analysis)
    to a holomorphic function on an open disk in the complex plane. This makes the machinery of complex analysis available. The (truncated) series can be used...
    48 KB (8,229 words) - 17:42, 2 July 2025
  • rational approximation through continued fractions CONTINUED FRACTIONS by C. D. Olds Look up simple continued fraction in Wiktionary, the free dictionary....
    69 KB (9,602 words) - 00:20, 21 July 2025
  • fraction [ 1 ; 2 , 2 , 2 , . . . ] {\displaystyle [1;2,2,2,...]} . This article considers only the case of periodic regular continued fractions. In other...
    17 KB (3,094 words) - 21:42, 1 April 2025
  • is the area of the four yellow triangles, and so on. Simplifying the fractions gives 1 + 1 4 + 1 16 + 1 64 + ⋯ , {\displaystyle 1+{\frac {1}{4}}+{\frac...
    34 KB (4,759 words) - 08:44, 17 July 2025
  • each ⁠ x {\displaystyle x} ⁠ in ⁠ E {\displaystyle E} ⁠ as a series of real or complex numbers. Equivalently, the partial sums s N ( x ) = ∑ n = 0 N f...
    78 KB (12,827 words) - 08:24, 9 July 2025
  • In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: ∑ n = 1 ∞ 1 n = 1 + 1 2 + 1 3 + 1 4 + 1 5 + ⋯...
    49 KB (6,224 words) - 21:21, 6 July 2025
  • Thumbnail for Mittag-Leffler's theorem
    Mittag-Leffler's theorem (category Theorems in complex analysis)
    Conversely, it can be used to express any meromorphic function as a sum of partial fractions. It is sister to the Weierstrass factorization theorem, which asserts...
    6 KB (1,036 words) - 04:59, 23 May 2025
  • Thumbnail for Gas blending for scuba diving
    decompression sickness. Methods used include batch mixing by partial pressure or by mass fraction, and continuous blending processes. Completed blends are...
    38 KB (5,143 words) - 05:13, 15 July 2025
  • list of articles that are considered real analysis topics. See also: glossary of real and complex analysis. Limit of a sequence Subsequential limit –...
    14 KB (1,603 words) - 13:55, 14 September 2024
  • Thumbnail for Derivative
    Derivative (category Mathematical analysis)
    {\displaystyle \mathbb {R} ^{2}} (in the sense that its partial derivatives all exist), but the converse is not true in general: the complex derivative only exists...
    58 KB (7,403 words) - 01:20, 3 July 2025
  • directly. The method works in many cases, and long ago it stimulated further development of the analytical theory of continued fractions. Here is a simple example...
    11 KB (1,766 words) - 20:51, 19 March 2025
  • function around a singularity Some coefficient involved in partial fraction decomposition A remainder in modular arithmetic Residue (TV series), an English...
    2 KB (246 words) - 23:58, 5 August 2023
  • Vector calculus identities (category Articles lacking in-text citations from August 2017)
    {\frac {\partial }{\partial x}},\ {\frac {\partial }{\partial y}},\ {\frac {\partial }{\partial z}}\end{pmatrix}}f={\frac {\partial f}{\partial x}}\mathbf...
    40 KB (6,570 words) - 12:32, 20 June 2025
  • Pi (redirect from Pi Continued Fraction)
    }}}}}}}}\end{aligned}}} Some approximations of pi include: Integers: 3 Fractions: Approximate fractions include (in order of increasing accuracy) ⁠22/7⁠, ⁠333/106⁠, ⁠355/113⁠...
    148 KB (17,241 words) - 16:02, 24 July 2025
  • Logarithmic derivative (category Complex analysis)
    In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula f ′ f {\displaystyle...
    10 KB (1,354 words) - 20:05, 15 June 2025
  • In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function...
    22 KB (3,550 words) - 08:56, 8 July 2025
  • _{\mathbb {R} ^{d}}\left({\frac {\partial F_{i}}{\partial x_{j}}}(\mathbf {r} ')-{\frac {\partial F_{j}}{\partial x_{i}}}(\mathbf {r} ')\right)K(\mathbf...
    44 KB (7,266 words) - 03:08, 20 April 2025
  • Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated...
    56 KB (6,953 words) - 07:51, 21 July 2025
  • Implicit function theorem (category Theorems in real analysis)
    condition on the partial derivatives (with respect to each yi ) at a point, the m variables yi are differentiable functions of the xj in some neighborhood...
    23 KB (3,821 words) - 05:35, 7 June 2025