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72 relations: Abramowitz and Stegun, Academic Press, Anatoli Prudnikov, Antiderivative, Bateman Manuscript Project, Bernoulli number, Bessel function, Beta function, Bibliotheca Teubneriana, Binomial coefficient, Bounded variation, Bronshtein and Semendyayev, Cauchy principal value, Cavalieri's quadrature formula, Closed-form expression, Computer algebra system, Constant of integration, CRC Press, David Bierens de Haan, Derivative, Differential Galois theory, Differentiation rules, Double factorial, Elementary function, Error function, Even and odd functions, Exponential function, Exponential integral, Function (mathematics), Gamma function, Gaussian integral, Gradshteyn and Ryzhik, Incomplete gamma function, Indefinite sum, Integral, Integral of secant cubed, Integral of the secant function, Interval (mathematics), Johann Bernoulli, Joseph Liouville, Laplace transform, Liouville's theorem (differential algebra), List of integrals of exponential functions, List of integrals of Gaussian functions, List of integrals of hyperbolic functions, List of integrals of inverse hyperbolic functions, List of integrals of inverse trigonometric functions, List of integrals of irrational functions, List of integrals of logarithmic functions, List of integrals of rational functions, ..., List of integrals of trigonometric functions, List of limits, List of mathematical series, Logarithmic integral function, Meijer G-function, Method of exhaustion, Nauka (publisher), Oleg Marichev, Probability density function, Risch algorithm, Sign function, Sinc function, Singularity (mathematics), Sophomore's dream, Special functions, Step function, Student's t-distribution, Symbolic integration, Trigonometric integral, Verlag Harri Deutsch, Wolfram Alpha, Wolfram Research. Expand index (22 more) »
Abramowitz and Stegun
Abramowitz and Stegun (AS) is the informal name of a mathematical reference work edited by Milton Abramowitz and Irene Stegun of the United States National Bureau of Standards (NBS), now the National Institute of Standards and Technology (NIST).
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Academic Press
Academic Press is an academic book publisher.
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Anatoli Prudnikov
Anatolii Platonovich Prudnikov (Анатолий Платонович Прудников; 14 January 1927 in Ulyanovsk, Russia – 10 January 1999) was a Russian mathematician.
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Antiderivative
In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.
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Bateman Manuscript Project
The Bateman Manuscript Project was a major effort at collation and encyclopedic compilation of the mathematical theory of special functions.
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Bernoulli number
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory.
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Bessel function
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are the canonical solutions of Bessel's differential equation for an arbitrary complex number, the order of the Bessel function.
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Beta function
In mathematics, the beta function, also called the Euler integral of the first kind, is a special function defined by for.
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Bibliotheca Teubneriana
The Bibliotheca Teubneriana, or Teubner editions of Greek and Latin texts, comprise the most thorough modern collection ever published of ancient (and some medieval) Greco-Roman literature.
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Binomial coefficient
In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient.
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Bounded variation
In mathematical analysis, a function of bounded variation, also known as function, is a real-valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense.
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Bronshtein and Semendyayev
Bronshtein and Semendyayev (often just Bronshtein or Bronstein) is the informal name of a comprehensive handbook of fundamental working knowledge of mathematics and table of formulas originally compiled by the Russian mathematician Ilya Nikolaevich Bronshtein and engineer Konstantin Adolfovic Semendyayev.
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Cauchy principal value
In mathematics, the Cauchy principal value, named after Augustin Louis Cauchy, is a method for assigning values to certain improper integrals which would otherwise be undefined.
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Cavalieri's quadrature formula
In calculus, Cavalieri's quadrature formula, named for 17th-century Italian mathematician Bonaventura Cavalieri, is the integral and generalizations thereof.
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Closed-form expression
In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations.
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Computer algebra system
A computer algebra system (CAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists.
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Constant of integration
In calculus, the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) on a connected domain is only defined up to an additive constant, the constant of integration.
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CRC Press
The CRC Press, LLC is a publishing group based in the United States that specializes in producing technical books.
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David Bierens de Haan
David Bierens de Haan (3 May 1822, Amsterdam – 12 August 1895, Leiden) was a Dutch mathematician and historian of science.
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Differential Galois theory
In mathematics, differential Galois theory studies the Galois groups of differential equations.
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Differentiation rules
This is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus.
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Double factorial
In mathematics, the double factorial or semifactorial of a number (denoted by) is the product of all the integers from 1 up to that have the same parity (odd or even) as.
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Elementary function
In mathematics, an elementary function is a function of one variable which is the composition of a finite number of arithmetic operations, exponentials, logarithms, constants, and solutions of algebraic equations (a generalization of ''n''th roots).
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Error function
In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion.
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Even and odd functions
In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses.
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Exponential function
In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.
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Exponential integral
In mathematics, the exponential integral Ei is a special function on the complex plane.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Gamma function
In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.
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Gaussian integral
The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function e−x2 over the entire real line.
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Gradshteyn and Ryzhik
Gradshteyn and Ryzhik (GR) is the informal name of a comprehensive table of integrals originally compiled by the Russian mathematicians I. S. Gradshteyn and I. M. Ryzhik.
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Incomplete gamma function
In mathematics, the upper incomplete gamma function and lower incomplete gamma function are types of special functions, which arise as solutions to various mathematical problems such as certain integrals.
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Indefinite sum
In mathematics the indefinite sum operator (also known as the antidifference operator), denoted by \sum _x or \Delta^, is the linear operator, inverse of the forward difference operator \Delta.
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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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Integral of secant cubed
The integral of secant cubed is a frequent and challenging indefinite integral of elementary calculus: There are a number of reasons why this particular antiderivative is worthy of special attention.
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Integral of the secant function
The integral of the secant function of trigonometry was the subject of one of the "outstanding open problems of the mid-seventeenth century", solved in 1668 by James Gregory.
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Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
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Johann Bernoulli
Johann Bernoulli (also known as Jean or John; – 1 January 1748) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family.
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Joseph Liouville
Joseph Liouville FRS FRSE FAS (24 March 1809 – 8 September 1882) was a French mathematician.
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Laplace transform
In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
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Liouville's theorem (differential algebra)
In mathematics, Liouville's theorem, originally formulated by Joseph Liouville in 1833 to 1841, places an important restriction on antiderivatives that can be expressed as elementary functions.
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List of integrals of exponential functions
The following is a list of integrals of exponential functions.
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List of integrals of Gaussian functions
In these expressions, is the standard normal probability density function, is the corresponding cumulative distribution function (where erf is the error function) and is Owen's T function.
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List of integrals of hyperbolic functions
The following is a list of integrals (anti-derivative functions) of hyperbolic functions.
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List of integrals of inverse hyperbolic functions
The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse hyperbolic functions.
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List of integrals of inverse trigonometric functions
The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse trigonometric functions.
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List of integrals of irrational functions
The following is a list of integrals (antiderivative functions) of irrational functions.
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List of integrals of logarithmic functions
The following is a list of integrals (antiderivative functions) of logarithmic functions.
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List of integrals of rational functions
The following is a list of integrals (antiderivative functions) of rational functions.
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List of integrals of trigonometric functions
The following is a list of integrals (antiderivative functions) of trigonometric functions.
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List of limits
This is a list of limits for common functions.
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List of mathematical series
This list of mathematical series contains formulae for finite and infinite sums.
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Logarithmic integral function
In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function.
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Meijer G-function
In mathematics, the G-function was introduced by as a very general function intended to include most of the known special functions as particular cases.
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Method of exhaustion
The method of exhaustion (methodus exhaustionibus, or méthode des anciens) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape.
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Nauka (publisher)
Nauka (Наука, lit. trans.: Science) is a Russian publisher of academic books and journals.
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Oleg Marichev
Oleg Igorevich Marichev (Олег Игоревич Маричев; born 7 September 1945 in Velikiye Luki, Russia) is a Russian mathematician.
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Probability density function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.
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Risch algorithm
In symbolic computation (or computer algebra), at the intersection of mathematics and computer science, the Risch algorithm is an algorithm for indefinite integration.
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Sign function
In mathematics, the sign function or signum function (from signum, Latin for "sign") is an odd mathematical function that extracts the sign of a real number.
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Sinc function
In mathematics, physics and engineering, the cardinal sine function or sinc function, denoted by, has two slightly different definitions.
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Singularity (mathematics)
In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability.
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Sophomore's dream
In mathematics, sophomore's dream is the pair of identities (especially the first) \int_0^1 x^\,dx &.
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Special functions
Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications.
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Step function
In mathematics, a function on the real numbers is called a step function (or staircase function) if it can be written as a finite linear combination of indicator functions of intervals.
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Student's t-distribution
In probability and statistics, Student's t-distribution (or simply the t-distribution) is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.
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Symbolic integration
In calculus, symbolic integration is the problem of finding a formula for the antiderivative, or indefinite integral, of a given function f(x), i.e. to find a differentiable function F(x) such that This is also denoted.
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Trigonometric integral
In mathematics, the trigonometric integrals are a family of integrals involving trigonometric functions.
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Verlag Harri Deutsch
The Verlag Harri Deutsch (VHD, HD) with headquarters in Frankfurt am Main, Germany, as well as in Zürich and Thun, Switzerland, was a German publishing house founded in 1961 and closed in 2013.
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Wolfram Alpha
Wolfram Alpha (also styled WolframAlpha, and Wolfram|Alpha) is a computational knowledge engine or answer engine developed by Wolfram Alpha LLC, a subsidiary of Wolfram Research.
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Wolfram Research
Wolfram Research is a private company that creates computational technology.
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References
[1] https://en.wikipedia.org/wiki/Lists_of_integrals
