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...ure''' is a form of [[Gaussian quadrature]] for approximating the value of integrals of the following kind: |first3=E. M. | last3=Gelbard | title = Gaussian quadratures for the integrals <math>\textstyle\int_0^\infty e^{-x^2} f(x) dx</math> and <math>\textstyle\ ...

[[image:Fresnel Integrals (Unnormalised).svg|250px|thumb| The '''Fresnel integrals''' ''S''(''x'') and ''C''(''x'') are two [[transcendental function]]s named ...

{{for|simple integrals of trigonometric functions|List of integrals of trigonometric functions}} In [[mathematics]], the '''trigonometric integrals''' are a [[indexed family|family]] of [[integral]]s involving [[trigonometr ...

...'' is one of a number of related functions defined as the value of certain integrals. Originally, they arose in connection with the problem of finding the [[ar ...nd the three [[Legendre form|Legendre canonical form]]s (i.e. the elliptic integrals of the first, second and third kind). ...

*{{Citation | last1=Scorer | first1=R. S. | title=Numerical evaluation of integrals of the form <math>I=\int^{x_2}_{x_{1}}f(x)e^{i\phi(x)}dx</math> and the tab ...

*{{dlmf|id=6|title=Exponential, Logarithmic, Sine, and Cosine Integrals|first=N. M. |last=Temme}} [[Category:Integrals]] ...

cf. [[#Integrals|integrals below]]. By the same token, the Euler polynomials are given by ==Integrals== ...

{{distinguish|text=[[List of integrals of exponential functions|other integrals]] of [[exponential function]]s}} | title = Asymptotic Expansions of Integrals ...

...rtial differential equations, and can also be given in terms of Euler-type integrals and [[line integral|contour integral]]s. ...Hugo |editor-last2=Moll |translator=Scripta Technica, Inc. |title=Table of Integrals, Series, and Products |publisher=[[Academic Press, Inc.]] |date=2015 |orig- ...

holding for positive ''z'' (and more generally wherever the integrals converge). Furthermore, ...Hugo |editor-last2=Moll |translator=Scripta Technica, Inc. |title=Table of Integrals, Series, and Products |publisher=Academic Press |date=2015 |orig-year=Octob ...

==Definite integrals involving the G-function== Among [[integral|definite integrals]] involving an arbitrary G-function one has: ...

...L. Glasser, R.A. Moore and T.C. Scott, ''Evaluation of Classes of Definite Integrals Involving Elementary Functions via Differentiation of Special Functions'', ...the function <math>T(m,s,x)</math> provide exact solutions to a number of integrals by repeated differentiation of the integral definition of the upper incompl ...

...on integral'''<ref>{{dlmf|id=7|title=Error Functions, Dawson's and Fresnel Integrals|first=N. M. |last=Temme}}</ref> ...

The Legendre functions can be written as contour integrals. For example, ...

...nal|last1=Glaisher|first1=James Whitbread Lee|title=On a class of definite integrals. Part II|journal=London, Edinburgh, and Dublin Philosophical Magazine and J ===Iterated integrals of the complementary error function=== ...

=={{anchor|sn|cn|dn|am}}Definition as inverses of elliptic integrals== ...st1=Byrd|first1=P.F.|last2=Friedman|first2=M.D.|title=Handbook of Elliptic Integrals for Engineers and Scientists|date=1971|publisher=Springer-Verlag|location=B ...

=== Relation to integrals of spin-weighted spherical harmonics === ...

====Bessel's integrals==== ...The definition may be extended to non-integer orders by one of Schläfli's integrals, for {{math|Re(''x'') > 0}}:<ref name=Temme /><ref>Watson, [https://books.g ...

...last=Blagouchine |title=Erratum and Addendum to "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results" ...first1=Olivier |last1=Espinosa|first2=Victor H. |last2=Moll|title= On Some Integrals Involving the Hurwitz Zeta Function: Part 1|journal=The Ramanujan Journal | ...

...1=Prudnikov|first2=Yu. A.|last2=Brychkov|first3=O. I.|last3=Marichev|title=Integrals & Series Volume 3: More Special Functions|publisher=Gordon and Breach|year= ...useful as it relates the higher-order hypergeometric functions in terms of integrals over the lower order ones<ref>{{harv|Slater|1966|loc=Equation (4.1.2)}}</re ...