Category:Special functions
functions which have established names and notations due to their importance in mathematics | |||||
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Pages in category "Category:Special functions"
- Category:Airy function
- Category:Anger function
- Category:Animations of special functions
- Category:Arithmetic functions
- Category:Bernoulli polynomials
- Category:Bessel functions
- Category:Blancmange function
- Category:Cantor function
- Category:Carotid–Kundalini function
- Category:Clausen functions
- Category:Coshc function
- Category:Dawson function
- Category:Dirichlet eta function
- Category:Distribution functions
- Category:Elliptic functions
- Category:Elliptic integral
- Category:Floor and ceiling
- Category:Fresnel integrals
- Category:Gamma and related functions
- Category:Griewank function
- Category:Gudermannian function
- Category:Heaviside function
- Category:Hurwitz zeta function
- Category:Hyperoperations
- Category:Integral functions
- Category:Lambert W function
- Category:Langevin function
- Category:Minkowski's question-mark function
- Category:Parabolic cylinder function
- Category:Polylogarithm
- Category:Riemann zeta function
- Category:Sigmoid functions
- Category:Signum function
- Category:Sinc function
- Category:Sinhc function
- Category:Sombrero function
- Category:Struve functions
- Category:Swirl function
- Category:Tanc function
- Category:Tanhc function
- Category:Thomae's function
- Category:Trigonometric functions
- Category:Voigt distribution
- Category:Wright Omega function
- Category:Zernike polynomials
- File:2022-07-30 18 07 05-Barnes-G zoomed.png
- File:2022-08-09 12 43 26-Barnes-G from -6 to 4.png
- File:A plot of the absolute value function abs(z) in the complex plane from -2-2i to 2+2i with colors created with the Mathematica function ComplexPlot3D.svg
- File:A plot of the Coshc function Cosh(z) in the complex plane from -2-2i to 2+2i with colors created with the Mathematica function ComplexPlot3D.svg
- File:A plot of the cothc function Cothc(z) in the complex plane from -2-2i to 2+2i with colors created with the Mathematica function ComplexPlot3D.svg
- File:A plot of the cschc function cschc(z) in the complex plane from -2-2i to 2+2i with colors created with the Mathematica function ComplexPlot3D.svg
- File:A plot of the cschc function cschc(z^2) in the complex plane from -2-2i to 2+2i with colors created with the Mathematica function ComplexPlot3D.svg
- File:A plot of the sechc function Sechc(z) in the complex plane from -2-2i to 2+2i with colors created with the Mathematica function ComplexPlot3D.svg
- File:A plot of the Sinhc function Sinhc(z) in the complex plane from -2-2i to 2+2i with colors created with the Mathematica function ComplexPlot3D.svg
- File:A plot of the tanhc function Tanhc(z) in the complex plane from -2-2i to 2+2i with colors created with the Mathematica function ComplexPlot3D.svg
- File:Absolute argument plot of the gamma function from z=-4 to 7 created in Mathematica 13.1.svg
- File:Askey Scheme hypergeom orthogonal polynomials.png
- File:Askey Scheme hypergeometric orthogonal polynomials.jpg
- File:Bernoulli polynomials no title.svg
- File:Bernstein polynomials.svg
- File:Besselo'.jpg
- File:Beta Function plotted in the complex plane in three dimensions with Mathematica 13.1's ComplexPlot3D.svg
- File:Bifurcation of Pearcey Integral.png
- File:Boubaker Polynomials (n=0-6), x=(-2,2).svg
- File:Boxcar function approximation.png
- File:Brjuno function.png
- File:Buchstab-function-graph-from-1-to-4.png
- File:Catastrophe Cusp of Pearcey Integral.png
- File:Chapman function.svg
- File:Chebyshev Zeros.svg
- File:Complex 3d plot the Bessel Clifford function evaluated at n=3 divided by 22 as C(3 divided 22,z) from -2-2i to 2+2i.svg
- File:Complex color plot of the Laguerre polynomial L n(x) with n as -1 divided by 9 and x as z to the power of 4 from -2-2i to 2+2i.svg
- File:Complex Plot of the regular Coulomb wave function from -2-2i to 2+2i in three dimensions created with Mathematica.svg
- File:Complex Riemann Xi.jpg
- File:Complex theta minus0point1times e i pi 0point1.jpg
- File:Cornu spiral.png
- File:Cosine integral.svg
- File:Coulomb F function plot.png
- File:Coulomb G function plot.png
- File:Dedekind Eta.jpg
- File:DickmanRho.png
- File:DiscriminantDelta.svg
- File:Easement Curve.png
- File:Easement curve.svg
- File:Eisenstein 10.jpg
- File:Eisenstein 12.jpg
- File:Eisenstein 14.jpg
- File:Eisenstein 4.jpg
- File:Eisenstein 6.jpg
- File:Eisenstein 8.jpg
- File:Euler function phi(x).svg
- File:Euler-bqf-2x2.PNG
- File:Faddeeva Function Domain Colouring Plot.svg
- File:Fadeeva Function.png
- File:Fibonacci continuous.png
- File:First derivatives of Neutralisers.png
- File:Gamma Function plotted in the complex plane in three dimensions with Mathematica ComplexPlot3D.svg
- File:Gamma function.gif
- File:Generalisation of Euler–Mascheroni constant.jpg
- File:Gjl-g a,b(x).png
- File:Gjl-w a(x).png
- File:Goodwin-Station integral Maple complex 3D plot.png
- File:Goodwin-staton integral derivative 2D plot.png
- File:Goodwin-staton integral derivative Re 3D plot.png
- File:Goodwin-staton integral Im complex 3D plot.png
- File:Goodwin-Staton integral Im density plot.JPG
- File:Goodwin-Staton Integral.png
- File:Graph of the Fabius function between 0 and 1.png
- File:Graph of the Fabius function.png
- File:Gudermannian-and-hyperbolics-table.png
- File:Hyperbolic and Circular Conic Sections Combined.png
- File:Hyperbolic functions-2.svg
- File:Hyperbolic functions.svg
- File:Incircles.JPG
- File:Infinite power tower.svg
- File:InfinitePowerTower.gif
- File:Integrand of Kelvin Wake Integral.png
- File:Irregular Coulomb wave function G plotted from 0 to 20 with repulsive and attractive interactions in Mathematica.svg
- File:J-Invariant.svg
- File:Jacobi am function and imverse 1.png
- File:Jacobi am function and imverse 2.png
- File:Jacobi theta 1.png
- File:Jacobi theta 2.png
- File:Jacobi theta 3.png
- File:Jacobi theta 4.png
- File:JacobiCN.png
- File:JacobiDN plot.png
- File:JacobiFunctionAbstract.png
- File:JacobiSN.png
- File:Kelvin Ship Wake Integrand contour Maple plot.png
- File:Kelvin Wakes contour plot.png
- File:Kelvin Wakes density plot.png
- File:KelvinBei.png
- File:KelvinBer.png
- File:KelvinKei.png
- File:KelvinKer.png
- File:KleinInvariantJ.jpg
- File:KleinjCont.png
- File:KleinjHSV.png
- File:Klff.png
- File:Knotenlinien sin xy RK02.svg
- File:KWW dist. funct. log fr.png
- File:KWW dist. funct. log.png
- File:KWW dist. function linear fr.png
- File:KWW dist. function linear.png
- File:Lambert Wien 001.png
- File:Legendre MRA filter.svg
- File:Legendre smoothing filter.png
- File:Lobatschewski.png
- File:Logarithmicpmf.svg
- File:LommelS1.png
- File:LommelS2.png
- File:Lucas continuous.png
- File:Maple density plot of Kelvin Wake.png
- File:MathieuC shortwave.gif
- File:MathieuCE.gif
- File:MathieuCPrime shortwave.gif
- File:MathieuFloquet.gif
- File:Mplwp arithmetic-geometric mean.svg
- File:Mplwp Dickman function log.svg
- File:Mplwp Dickman function.svg
- File:Mplwp dilogarithm complex.svg
- File:Mplwp dilogarithm.svg
- File:Mplwp dirichlet beta.svg
- File:Mplwp Fabius function.svg
- File:Neutralisers.png
- File:NevilleThetaC Maple complex plot 01.png
- File:NevilleThetaC.png
- File:NevilleThetaD Maple complex plot.png
- File:NevilleThetaD.png
- File:NevilleThetaN Maple complex plot.png
- File:NevilleThetaN.png
- File:NevilleThetaS Maple complex plot.png
- File:NevilleThetaS.png
- File:Normal cumulative distribution function complex plot in Mathematica 13.1 with ComplexPlot3D.svg
- File:Pearcey Integral 3D Maple plot.png
- File:Pearcey Integral Maple contour plot.png
- File:Pearcey Integral Maple density plot.png
- File:Pibmasterplot fr.png
- File:Pibmasterplot.png
- File:Plot of gamma function in complex plane in 3D with color and legend and 1000 plot points created with Mathematica.svg
- File:Plot of gamma function in the complex plane from -2-i to 6+2i with colors created in Mathematica.svg
- File:Plot of logarithmic gamma function in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of polygamma function in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1.svg
- File:Plot of the Airy function Ai(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Airy function Bi(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Anger function J v(z) with n=2 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the arctangent function arctan(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica function ComplexPlot3D.svg
- File:Plot of the arctangent function of z^2 arctan(z^2) in the complex plane from -2-2i to 2+2i with colors created with Mathematica function ComplexPlot3D.svg
- File:Plot of the arithmetic-geometric mean function with 1 and z in the complex plane from -2-2i to 2+2i with colors created with Mathematica function ComplexPlot3D.svg
- File:Plot of the Barnes G aka double gamma function G(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Bateman function k n(z) with n=7 in the complex plane from -2-2i to 2+2i with colors created with Mathematica function ComplexPlot3D.svg
- File:Plot of the Bessel function of the first kind J n(z) with n=0.5 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Bessel function of the second kind Y n(z) with n=0.5 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Chebyshev polynomial of the first kind T n(x) with n=5 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the complementary error function Erfc(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the complex argument function arg(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica function ComplexPlot3D.svg
- File:Plot of the confluent hypergeometric function 0F1(;a;z) with a=sqrt(2) and the input=z^2 as 0F1(;sqrt(2);z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1.svg
- File:Plot of the cosine integral function Ci(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Dawson integral function F(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the derivative of the Airy function Ai'(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the derivative of the Airy function Bi'(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the derivative of the Scorer function Gi'(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the derivative of the Scorer function Hi'(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the error function Erf(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the exponential integral function E n(z) with n=2 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the exponential integral function Ei(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Fox H function H((((a 1,α 1),...,(a n,α n)),((a n+1,α n+1),...,(a p,α p)),(((b 1,β 1),...,(b m,β m)),in ((b m+1,β m+1),...,(b q,β q))),z) with H(((),()),(((-1,½)),()),z).svg
- File:Plot of the Fresnel auxillary function F(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Fresnel auxillary function G(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Fresnel integral function C(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Fresnel integral function S(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Gegenbauer polynomial C n^(m)(x) with n=10 and m=1 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the generalized hypergeometric function pFq(a b z) with a=(2,4,6,8) and b=(2,3,5,7,11) in the complex plane from -2-2i to 2+2i created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Hankel function of the first kind H n^(1)(z) with n=-0.5 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Hankel function of the second kind H n^(2)(z) with n=-0.5 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the hyperbolic cosine integral function Chi(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the hyperbolic sine integral function Shi(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the hypergeometric function 2F1(a,b; c; z) with a=2 and b=3 and c=4 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the imaginary error function Erfi(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Jacobi polynomial function P n^(a,b) with n=10 and a=2 and b=2 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Kelvin function bei(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Kelvin function ber(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Kelvin function kei(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Kelvin function ker(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Kummer confluent hypergeometric function 1F1(a;b;z) with a=1 and b=2 and input z² with 1F1(1,2,z²) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1.svg
- File:Plot of the Legendre function of the second kind Q n(x) with n=0.5 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Legendre polynomial P n(x) with n=0.5 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the logarithmic integral function li(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Meiger G function G(((a 1,...,a n),(a n+1,...,a p)),((b 1,...,b m),(b m+1,...,b q)),z) input ((½),()),((⅓),()) in the complex plane from -2-2i to 2+2i.svg
- File:Plot of the modified Struve function L n(z) with n=2 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the regularized incomplete gamma function Q(2,z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Scorer function Gi(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Scorer function Hi(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the sine integral function Si(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the spherical Bessel function of the first kind j n(z) with n=0.5 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the spherical Bessel function of the second kind y n(z) with n=0.5 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the spherical Hankel function of the first kind h n^(1)(z) with n=-0.5 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the spherical Hankel function of the second kind h n^(2)(z) with n=-0.5 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the spherical harmonic Y l^m(theta,phi) with n=2 and m=1 and phi=pi in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Struve function H n(z) with n=2 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Weber function E v(z) with n=2 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Whittaker function M k,m(z) with k=2 and m=½ in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Plot of the Whittaker function W k,m(z) with k=2 and m=½ in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg
- File:Q function complex plot plotted with Mathematica 13.1 ComplexPlot3D.svg
- File:Qsin.gif
- File:Raised Cosine.png
- File:Raiz cubica.png
- File:Raíz cúbica de un quebrado común.png
- File:Regular Coulomb wave function F plotted from 0 to 20 with repulsive and attractive interactions in Mathematica.svg
- File:Riemann Siegel Theta 1.jpg
- File:Riemann Siegel Theta 2.jpg
- File:Riemann Siegel Theta 3.jpg
- File:Rogers dilogarithm.svg
- File:Rogers400.png
- File:RogersRamanujan400.png
- File:Second derivatives of Neutralisers.png
- File:Sigmoid function 02.png
- File:Singularity function.jpg
- File:Solution-set-2.png
- File:Stokes set of Pearcey Integral.png
- File:SwaIntegral Maple density plotllowtail.png
- File:Swallowtail integral Bifurcation catastrophe.png
- File:Swallowtail integral catastrophe for z=0.png
- File:Swallowtail Integral Maple 3D plot.png
- File:Swallowtail Integral Maple contour plot.png
- File:Swallowtail integral Stokes set 1.png
- File:Swallowtail integral Stokes set 2.png
- File:The binary logarithm function lg(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The cardinal cosecant function cscc(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The cardinal hyperbolic cosecant function cschc(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The cardinal hyperbolic cosine function coshc(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The cardinal hyperbolic cotangent function cothc(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The cardinal hyperbolic secant function sechc(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The cardinal hyperbolic sine function sinhc(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The cardinal hyperbolic tangent function tanhc(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The cardinal sine function sinc(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The cosecant function csc(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The cosine function cos(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The cotangent function cot(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The decimal logarithm function logbase(10,z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The exponential function e^z plotted in the complex plane from -2-2i to 2+2i.svg
- File:The hyperbolic cosecant function csch(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The hyperbolic cosine function cosh(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The hyperbolic cottangent function coth(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The hyperbolic secant function sech(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The hyperbolic sine function sinh(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The hyperbolic tangent function tanh(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The natural logarithm function ln(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The product logarithm Lambert W function plotted in the complex plane from -2-2i to 2+2i.svg
- File:The product logarithm Lambert W function W 2(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The secant function sec(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The sine function sin(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The tangent function tan(z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:The ternary logarithm function logbase(3,z) plotted in the complex plane from -2-2i to 2+2i.svg
- File:Tosinus.png
- File:Von Bertalanffy function.svg
- File:Weber3d.png
- File:WhittakerM 01.png
- File:WhittakerM 02.png
- File:X raised by x.svg
- File:X to x power showing minimum.svg
- File:Чёртова лестница.png
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