User contributions
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- 21:15, 4 October 2014 (diff | hist) . . (+117) . . N Euler E (Created page with "The Euler polynomials $E_n(x)$ are defined by $$\dfrac{2e^{xt}}{e^t+1} = \sum_{k=0}^{\infty} \dfrac{E_n(x)t^n}{n!}.$$")
- 21:14, 4 October 2014 (diff | hist) . . (+140) . . N Bernoulli B (Created page with "Bernoulli polynomials $B_n$ are defined by the formula $$\dfrac{te^{xt}}{e^t-1} = \displaystyle\sum_{k=0}^{\infty} \dfrac{B_n(x) t^n}{n!}.$$")
- 21:12, 4 October 2014 (diff | hist) . . (+29) . . Main Page (→Polynomials)
- 21:12, 4 October 2014 (diff | hist) . . (+100) . . N Bessel polynomial (Created page with "The Bessel polynomials are defined by $$y_n(x) = {}_2F_0 \left( -n, 1+n;-; -\dfrac{1}{2}x \right).$$")
- 21:11, 4 October 2014 (diff | hist) . . (+28) . . Main Page (→Polynomials)
- 21:10, 4 October 2014 (diff | hist) . . (+136) . . N Bateman F (Created page with "The Bateman polynomials are defined by $$Z_n(x) = {}_2F_2(-n,n+1;1;1;x),$$ where ${}_2F_2$ is a generalized hypergeometric function.")
- 21:09, 4 October 2014 (diff | hist) . . (+30) . . Main Page (→Polynomials)
- 21:05, 4 October 2014 (diff | hist) . . (+266) . . N Legendre P (Created page with "The Legendre polynomials are defined by the recurrence $$P_n(x) = \dfrac{1}{2^nn!}\dfrac{d^n}{dx^n}(x^2-1)^n; n=0,1,2,\ldots$$ $$\begin{array}{ll} P_0(x) &= 1 \\ P_1(x) &= x \...")
- 21:03, 4 October 2014 (diff | hist) . . (+128) . . N Cosine integral (Created page with "The cosine integral is defined by $$\mathrm{Ci}(z) = -\displaystyle\int_z^{\infty} \dfrac{\cos t}{t} dt ; |mathrm{arg} z|<\pi.$$")
- 21:02, 4 October 2014 (diff | hist) . . (+118) . . N Sine integral (Created page with "The sine integral is defined by $$\mathrm{Si}(z) = \displaystyle\int_0^z \dfrac{\sin t}{t} dt; |\mathrm{arg} z|<\pi.$$")
- 21:01, 4 October 2014 (diff | hist) . . (+50) . . Main Page (→Special functions)
- 21:00, 4 October 2014 (diff | hist) . . (-98) . . Exponential integral E
- 20:58, 4 October 2014 (diff | hist) . . (+125) . . Exponential integral E
- 20:57, 4 October 2014 (diff | hist) . . (+6) . . Logarithmic integral
- 20:57, 4 October 2014 (diff | hist) . . (+250) . . N Logarithmic integral (Created page with "The logarithmic integral is $$\mathrm{li}(x) = \displaystyle\int_0^x \dfrac{dt}{\log(t)},$$ where $\log$ denotes the logarithm. It can be shown that $\mathrm{li}(x)=\mathr...")
- 20:55, 4 October 2014 (diff | hist) . . (+211) . . N Exponential integral E (Created page with "The exponential integrals are $$\mathrm{Ei}(x) = \int_{-\infty}^x \dfrac{e^t}{t} dt$$ and $$E_1(x) = \int_x^{\infty} \dfrac{e^{-t}}{t} dt.$$ Simple properties of integrals imp...")
- 20:53, 4 October 2014 (diff | hist) . . (+37) . . Main Page (→Special functions)
- 20:53, 4 October 2014 (diff | hist) . . (+436) . . N Jacobi P (Created page with "The Jacobi polynomial $P_n^{(\alpha,\beta)}$ is the coefficient of $t^n$ in the expansion of $$\dfrac{2^{\alpha+\beta}}{\sqrt{1-2xt+t^2}\left(1-t+ \sqrt{1-2xt+t^2} \right)^{\...")
- 20:49, 4 October 2014 (diff | hist) . . (+29) . . Main Page (→Polynomials)
- 20:48, 4 October 2014 (diff | hist) . . (-209) . . Gegenbauer C
- 20:47, 4 October 2014 (diff | hist) . . (+2,005) . . m Gegenbauer C (→Properties)
- 20:42, 4 October 2014 (diff | hist) . . (+1,104) . . N Gegenbauer C (Created page with "The Gegenbauer polynomial of degree $n$ and order $\lambda$ is the coefficient of $t^n$ in the expansion of $\dfrac{1}{(1-2xt+t^2)^{\lambda}}$ in the sense that $$\dfrac{1}{(...")
- 20:37, 4 October 2014 (diff | hist) . . (+33) . . Main Page (→Polynomials)
- 20:24, 4 October 2014 (diff | hist) . . (+260) . . Laguerre L (→Properties)
- 19:20, 4 October 2014 (diff | hist) . . (+500) . . Laguerre L
- 19:19, 4 October 2014 (diff | hist) . . (-16) . . Laguerre L (→Properties)
- 19:18, 4 October 2014 (diff | hist) . . (+379) . . Laguerre L
- 19:16, 4 October 2014 (diff | hist) . . (0) . . Laguerre L
- 19:16, 4 October 2014 (diff | hist) . . (0) . . Laguerre L
- 19:16, 4 October 2014 (diff | hist) . . (+520) . . Laguerre L
- 19:12, 4 October 2014 (diff | hist) . . (+533) . . N Laguerre L (Created page with "Laguerre's equation is $$x\dfrac{y^2x}{dx^2}+(1-x)\dfrac{dy}{dx}+ny=0.$$ One of the solutions of this differential equations are the Laguerre polynomials $$L_n(x) = \displayst...")
- 16:35, 4 October 2014 (diff | hist) . . (+28) . . Main Page
- 16:34, 4 October 2014 (diff | hist) . . (+122) . . N Hurwitz zeta (Created page with "The Hurwitz zeta function is defined for $\Re(s)>1$, $$\zeta(s,a)= \displaystyle\sum_{n=0}^{\infty} \dfrac{1}{(n+a)^s}.$$")
- 16:31, 4 October 2014 (diff | hist) . . (+29) . . Main Page (→Special functions in number theory)
- 16:30, 4 October 2014 (diff | hist) . . (+682) . . N Mangoldt (Created page with "The Mangoldt function is defined by the formula $$\Lambda(n) = \left\{ \begin{array}{ll} \log p &; n=p^k \mathrm{\hspace{2pt}for\hspace{2pt}some\hspace{2pt}prime\hspace{2pt}}p...")
- 16:26, 4 October 2014 (diff | hist) . . (0) . . Main Page (→Special functions in number theory)
- 16:26, 4 October 2014 (diff | hist) . . (+28) . . Main Page (→Special functions in number theory)
- 16:22, 4 October 2014 (diff | hist) . . (-46) . . Euler totient (→Properties)
- 16:21, 4 October 2014 (diff | hist) . . (+403) . . Euler totient (→Properties)
- 16:15, 4 October 2014 (diff | hist) . . (+555) . . N Liouville lambda (Created page with "The Liouville function is defined by the formula $$\lambda(n) = (-1)^{\Omega(n)},$$ where $\Omega(n)$ indicates the number of prime factors of $n$, counted with multiplicity....")
- 16:13, 4 October 2014 (diff | hist) . . (+1) . . Mertens function (current)
- 16:13, 4 October 2014 (diff | hist) . . (+996) . . Möbius
- 16:13, 4 October 2014 (diff | hist) . . (+30) . . N Mobius function (Tom moved page Mobius function to Möbius function) (current)
- 16:13, 4 October 2014 (diff | hist) . . (0) . . m Möbius (Tom moved page Mobius function to Möbius function)
- 16:11, 4 October 2014 (diff | hist) . . (+1) . . N Möbius (Created page with "a")
- 16:11, 4 October 2014 (diff | hist) . . (+128) . . N Mertens function (Created page with "Merten's function is defined by the formula $$M(n) = \displaystyle\sum_{k=1}^n \mu(k),$$ where $\mu$ is the Mobius function.")
- 16:10, 4 October 2014 (diff | hist) . . (+55) . . Main Page (→Special functions in number theory)
- 16:10, 4 October 2014 (diff | hist) . . (+27) . . Main Page (→Special functions in number theory)
- 16:09, 4 October 2014 (diff | hist) . . (+38) . . Main Page
- 16:01, 4 October 2014 (diff | hist) . . (+27) . . Main Page (→Special functions)
- 16:00, 4 October 2014 (diff | hist) . . (+525) . . Euler totient
- 15:58, 4 October 2014 (diff | hist) . . (+399) . . Euler totient
- 15:56, 4 October 2014 (diff | hist) . . (+185) . . N Euler totient (Created page with "Euler's totient function (sometimes called Euler's $\phi$ function) is the function <br /> <center>$\phi(n) =$ # of positive integers $\leq n$ that are relatively prime to $n$...")
- 15:53, 4 October 2014 (diff | hist) . . (+21) . . N Tangent function (Tom moved page Tangent function to Tangent) (current)
- 15:53, 4 October 2014 (diff | hist) . . (0) . . m Tangent (Tom moved page Tangent function to Tangent)
- 15:53, 4 October 2014 (diff | hist) . . (+29) . . Main Page
- 15:52, 4 October 2014 (diff | hist) . . (+20) . . N Cosine function (Tom moved page Cosine function to Cosine) (current)
- 15:52, 4 October 2014 (diff | hist) . . (0) . . m Cosine (Tom moved page Cosine function to Cosine)
- 15:52, 4 October 2014 (diff | hist) . . (+18) . . N Sine function (Tom moved page Sine function to Sine) (current)
- 15:52, 4 October 2014 (diff | hist) . . (0) . . m Sine (Tom moved page Sine function to Sine)
- 15:51, 4 October 2014 (diff | hist) . . (+126) . . N Tangent (Created page with "The tangent function is defined as the ratio of the sine and cosine functions: $$\tan(x) = \dfrac{\sin(x)}{\cos(x)}.$$")
- 15:47, 4 October 2014 (diff | hist) . . (0) . . Mills' constant
- 15:47, 4 October 2014 (diff | hist) . . (+293) . . N Mills' constant (Created page with "Mills' constant is the smallest positive real number $M$ such that $\left\lfloor A^{3^n} \right\rfloor$ is prime for every positive $n$. =References= [http://www.ams.org/jou...")
- 15:45, 4 October 2014 (diff | hist) . . (+900) . . Pi
- 15:36, 4 October 2014 (diff | hist) . . (+272) . . N Pi (Created page with "=References= [http://math.stackexchange.com/questions/3198/proof-that-pi-is-constant-the-same-for-all-circles-without-using-limits Proof that $\pi$ is constant for all circles...")
- 15:32, 4 October 2014 (diff | hist) . . (+56) . . Main Page (→$q$-Calculus)
- 15:31, 4 October 2014 (diff | hist) . . (+16) . . Main Page
- 15:30, 4 October 2014 (diff | hist) . . (+142) . . Prime counting
- 15:29, 4 October 2014 (diff | hist) . . (-20) . . Prime counting
- 15:29, 4 October 2014 (diff | hist) . . (+339) . . Prime counting
- 02:29, 3 October 2014 (diff | hist) . . (+248) . . E
- 02:26, 3 October 2014 (diff | hist) . . (+96) . . E
- 02:17, 3 October 2014 (diff | hist) . . (+240) . . N Continued fraction (Created page with "Let $x \in \mathbb{R}$. Then $x$ has a continued fraction expansion, notated $x=[a_0;a_1,a_2,\ldots]$ if $x$ can be represented as $$x = a_0 + \dfrac{1}{a_1+\dfrac{1}{a_2+\dfr...") (current)
- 02:07, 3 October 2014 (diff | hist) . . (+395) . . N Minkowski question mark (Created page with "If $x \in \mathbb{R}$ is irrational with continued fraction expansion $x=[a_0;a_1,a_2,\ldots]$ then define $$?(x) = a_0 + 2 \displaystyle\sum_{n=1}^{\infty} \dfrac{(-1)^{n...")
- 01:35, 3 October 2014 (diff | hist) . . (+139) . . N Graph (Created page with "A graph $G$ is a set $G=\{V,E\}$ where $V$ is a set called the vertices of $G$ and $E \subset V \times V$ is a set called the edges of $G$.") (current)
- 23:43, 2 October 2014 (diff | hist) . . (+120) . . N Khinchin's constant (Created page with " =References= [http://dualaud.net/talks/pdf/Khinchin-constant-12-Sept-2014-MST-Analysis-Seminar.pdf Khinchin's Constant]")
- 21:31, 2 October 2014 (diff | hist) . . (+2) . . Pochhammer
- 21:31, 2 October 2014 (diff | hist) . . (+125) . . N Pochhammer (Created page with "$$(a)_0 = 1$$ $$(a)_n=a(a+1)(a+2)\ldots(a+n-1)=\dfrac{\Gamma(a+n)}{\Gamma(a)},$$ where $\Gamma$ denotes the [gamma function].")
- 21:28, 2 October 2014 (diff | hist) . . (+242) . . N Q-Beta function (Created page with "$$B_q(a,b) = \dfrac{\Gamma_q(a)\Gamma_q(b)}{\Gamma_q(a+b)}$$ $$B_q(a,b) = \displaystyle\int_0^1 \dfrac{t^{a-1}(tq;q)_{\infty}}{(tq^b;q)_{\infty}} d_q t$$ =References= [http:/...")
- 21:26, 2 October 2014 (diff | hist) . . (+77) . . Q-Gamma (→References)
- 21:23, 2 October 2014 (diff | hist) . . (+13) . . Q-Gamma (→Properties)
- 21:16, 2 October 2014 (diff | hist) . . (+123) . . N Factorial (Created page with "Let $n$ be an integer. Then the factorial of $n$, written $n!$, is the integer $$n!=n(n-1)(n-2)\ldots 3 \cdot 2 \cdot 1.$$")
- 21:15, 2 October 2014 (diff | hist) . . (+20) . . Main Page (→Special functions)
- 21:15, 2 October 2014 (diff | hist) . . (+38) . . Gamma (→Recurrence)
- 21:13, 2 October 2014 (diff | hist) . . (+676) . . Gamma (→Other formulas)
- 21:09, 2 October 2014 (diff | hist) . . (+109) . . N Euler-Mascheroni constant (Created page with "$$\gamma = \lim_{n \rightarrow \infty} 1 + \dfrac{1}{2} + \ldots + \dfrac{1}{n}-\log(n) = 0.577215664901532$$")
- 20:32, 2 October 2014 (diff | hist) . . (+8) . . Cosine
- 20:32, 2 October 2014 (diff | hist) . . (+38) . . Sine
- 20:31, 2 October 2014 (diff | hist) . . (+49) . . Cosine
- 20:31, 2 October 2014 (diff | hist) . . (+13) . . Cosine
- 20:30, 2 October 2014 (diff | hist) . . (+90) . . N Cosine (Created page with "The cosine function is the unique solution of the differential equation $$y''=-y;y(0)=1.$$")
- 16:38, 2 October 2014 (diff | hist) . . (+40) . . N Integration by parts (Created page with "$$\int_a^b u dv = uv|_a^b - \int v du.$$")
- 01:01, 1 October 2014 (diff | hist) . . (+117) . . Main Page (→Zeta functions)
- 01:00, 1 October 2014 (diff | hist) . . (+780) . . Main Page (→Zeta functions)
- 00:53, 1 October 2014 (diff | hist) . . (+70) . . N Polylogarithm (Created page with "$$\mathrm{Li}_s(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{k^s}$$")
- 00:49, 1 October 2014 (diff | hist) . . (+791) . . N Beta (Created page with "$$B(x,y)=\displaystyle\int_0^1 t^{x-1}(1-t)^{y-1}dt$$ =Properties= <div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> $B(x,y)=...")
- 00:44, 1 October 2014 (diff | hist) . . (+20) . . Main Page (→Special functions)
- 00:41, 1 October 2014 (diff | hist) . . (+502) . . Main Page (→Special functions)
- 21:32, 25 September 2014 (diff | hist) . . (+29) . . Hermite (probabilist)
- 18:28, 23 September 2014 (diff | hist) . . (+2) . . Secant zeta function
- 18:28, 23 September 2014 (diff | hist) . . (+75) . . Secant zeta function
- 18:27, 23 September 2014 (diff | hist) . . (+71) . . N Secant zeta function (Created page with "=References= [http://arxiv.org/pdf/1304.3922.pdf Secant zeta functions]")
- 18:26, 23 September 2014 (diff | hist) . . (+31) . . Main Page
- 06:08, 23 September 2014 (diff | hist) . . (+920) . . Gamma
- 05:58, 23 September 2014 (diff | hist) . . (+6) . . Main Page (→Tools from calculus)
- 05:58, 23 September 2014 (diff | hist) . . (+25) . . Main Page (→Tools from calculus)
- 05:55, 23 September 2014 (diff | hist) . . (+144) . . Gamma
- 05:55, 23 September 2014 (diff | hist) . . (+49) . . Apéry's constant
- 05:55, 23 September 2014 (diff | hist) . . (+410) . . Gamma (→Properties)
- 05:49, 23 September 2014 (diff | hist) . . (+641) . . N Apéry's constant (Created page with "Apéry's constant is the value $\zeta(3)$, where $\zeta$ denotes the Riemann zeta function. This constant is notable because it is known in general that for integers $n$,...")
- 02:18, 23 September 2014 (diff | hist) . . (0) . . Q-Pochhammer
- 02:15, 23 September 2014 (diff | hist) . . (+156) . . N Q-Hermite polynomial (Created page with "=References= [http://arxiv.org/pdf/1101.2875v4.pdf On the $q$-Hermite polynomials and their relationship with some other families of orthogonal polynomials]")
- 02:14, 23 September 2014 (diff | hist) . . (+56) . . Main Page (→Special functions)
- 17:27, 21 September 2014 (diff | hist) . . (+143) . . N E (Created page with "The number $e$ can be defined in the following way: let $f$ be the unique solution of the initial value problem $$y'=y;y(0)=1,$$ then $e=f(1)$.")
- 17:26, 21 September 2014 (diff | hist) . . (+308) . . Fransén–Robinson constant
- 17:05, 21 September 2014 (diff | hist) . . (+147) . . N Fransén–Robinson constant (Created page with "The Fransén–Robinson constant is defined to be the number $F$ given by the formula $$F = \displaystyle\int_0^{\infty} \dfrac{1}{\Gamma(x)} dx.$$")
- 17:05, 21 September 2014 (diff | hist) . . (+39) . . Main Page (→Special constants)
- 11:01, 21 September 2014 (diff | hist) . . (+1) . . Gamma
- 11:01, 21 September 2014 (diff | hist) . . (+337) . . Gamma (→Properties)
- 03:49, 14 September 2014 (diff | hist) . . (+220) . . Hermite (probabilist)
- 01:34, 14 September 2014 (diff | hist) . . (+943) . . Hermite (probabilist)
- 01:30, 14 September 2014 (diff | hist) . . (+4) . . Hermite (probabilist)
- 01:29, 14 September 2014 (diff | hist) . . (+308) . . N Hermite (probabilist) (Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> The Hermite polynomials $H_n$ satisfy the Rodrigues' formula $$H_n(t) = (-1)...")
- 01:27, 14 September 2014 (diff | hist) . . (+29) . . Main Page
- 04:54, 12 September 2014 (diff | hist) . . (-1) . . Main Page (→Special functions)
- 03:08, 12 September 2014 (diff | hist) . . (+180) . . N Prime counting (Created page with "The prime counting function $\pi \colon \mathbb{R} \rightarrow \mathbb{Z}^+$ is defined by the formula $$\pi(x) = \{\mathrm{number \hspace{2pt} of \hspace{2pt} primes} \leq x...")
- 03:07, 12 September 2014 (diff | hist) . . (+34) . . Main Page (→Special functions)
- 02:59, 12 September 2014 (diff | hist) . . (+24) . . Main Page (→Special functions)
- 10:20, 10 September 2014 (diff | hist) . . (+124) . . N Lambert W (Created page with "Let $z \in \mathbb{C}$ and define the Lambert $W$ function by the relation $z=W(z)e^{W(z)}$. This function has two branches.")
- 20:22, 31 August 2014 (diff | hist) . . (-3) . . Main Page (→Other)
- 20:22, 31 August 2014 (diff | hist) . . (+118) . . Main Page
- 00:55, 29 August 2014 (diff | hist) . . (+28) . . Q-Bessel functions
- 00:55, 29 August 2014 (diff | hist) . . (+22) . . Main Page (→Special functions)
- 00:53, 29 August 2014 (diff | hist) . . (+40) . . Main Page (→Special functions)
- 00:53, 29 August 2014 (diff | hist) . . (+706) . . N Q-Bessel functions (Created page with "The three Jackson $q$-Bessel functions are $$J_{\nu}^{(1)}(x;q) = \dfrac{(q^{\nu+1};q)_{\infty}}{(q;q)_{\infty}} \left( \dfrac{x}{2} \right)^{\nu} {}_2\Phi_1\left(0,0;q^{\nu+1...")
- 05:35, 3 August 2014 (diff | hist) . . (+27) . . Main Page (→Special constants)
- 01:00, 3 August 2014 (diff | hist) . . (+282) . . Airy Bi
- 00:58, 3 August 2014 (diff | hist) . . (+100) . . N Airy Bi (Created page with "The Airy functions $\mathrm{Ai}$ and $\mathrm{Bi}$ solve the differential equation $$y'' - xy = 0.$$")
- 00:57, 3 August 2014 (diff | hist) . . (+324) . . N Exponential (Created page with "Let $a$ be constant. Exponential functions are of the form $$f(x)=a^x.$$ The most commonly used exponential function is $e^x$, where $e$ is the E | base of the natural logar...")
- 00:55, 3 August 2014 (diff | hist) . . (+31) . . Main Page (→Special functions)
- 00:55, 3 August 2014 (diff | hist) . . (+293) . . Main Page
- 00:49, 3 August 2014 (diff | hist) . . (+6) . . Ihara zeta function (→References)
- 00:49, 3 August 2014 (diff | hist) . . (+157) . . Ihara zeta function (→References)
- 00:46, 3 August 2014 (diff | hist) . . (+104) . . N Euler product (Created page with "An Euler product is a way to represent a Dirichlet series as an infinite product over prime numbers.")
- 00:45, 3 August 2014 (diff | hist) . . (+330) . . Riemann zeta
- 00:42, 3 August 2014 (diff | hist) . . (+4) . . Ihara zeta function
- 00:42, 3 August 2014 (diff | hist) . . (+568) . . N Ihara zeta function (Created page with "Let $X$ be a finite graph. The Ihara zeta function is given by the formula $$\zeta_X(t) = \displaystyle\prod_{[C]} \dfrac{1}{1-t^{|C|}},$$ where $[C]$ is the set of equiva...")
- 00:37, 3 August 2014 (diff | hist) . . (+30) . . Main Page (→Special functions)
- 11:03, 28 July 2014 (diff | hist) . . (+41) . . Main Page (→Special functions)
- 22:51, 27 July 2014 (diff | hist) . . (+24) . . Main Page (→Special functions)
- 22:50, 27 July 2014 (diff | hist) . . (+9) . . Dedekind eta
- 18:43, 27 July 2014 (diff | hist) . . (+33) . . Main Page (→Special functions)
- 18:41, 27 July 2014 (diff | hist) . . (-58) . . Q-Binomial
- 18:41, 27 July 2014 (diff | hist) . . (+789) . . Q-Binomial (→Properties)
- 18:32, 27 July 2014 (diff | hist) . . (-74) . . Q-Binomial (→Properties)
- 18:32, 27 July 2014 (diff | hist) . . (+411) . . Q-Binomial
- 18:21, 27 July 2014 (diff | hist) . . (0) . . Main Page (→Special functions)
- 18:20, 27 July 2014 (diff | hist) . . (+104) . . N Q-Binomial (Created page with "$${n \brack m}_q = \dfrac{(q;q)_n}{(q;q)m(q;q)_{n-m}},$$ where $(q;q)_k$ is the q-Pochhammer symbol.")
- 18:18, 27 July 2014 (diff | hist) . . (+1) . . Main Page (→Special functions)
- 18:17, 27 July 2014 (diff | hist) . . (0) . . Q-factorial
- 18:17, 27 July 2014 (diff | hist) . . (+189) . . N Q-factorial (Created page with "The $q$-Factorial is defined for a non-negative integer $k$ by $$[k]_q!=1(1+q)(1+q+q^2)\ldots(1+q+\ldots+q^{k-1})=\dfrac{(q;q)_k}{(1-q)^k},$$ where $(q;q)_k$ is the q-Pochha...")
- 18:14, 27 July 2014 (diff | hist) . . (+38) . . Main Page (→Special functions)
- 18:12, 27 July 2014 (diff | hist) . . (+1) . . Main Page
- 18:09, 27 July 2014 (diff | hist) . . (+608) . . N Format notes (Created page with "This is a list of common code templates and styles we use at specialfunctionswiki. =Theorem/proof box template= The code <pre><div class="toccolours mw-collapsible mw-collaps...")
- 18:08, 27 July 2014 (diff | hist) . . (+15) . . MediaWiki:Sidebar
- 18:08, 27 July 2014 (diff | hist) . . (-14) . . MediaWiki:Sidebar
- 18:08, 27 July 2014 (diff | hist) . . (+188) . . N MediaWiki:Sidebar (Created page with " * navigation ** mainpage|mainpage-description ** recentchanges-url|recentchanges ** randompage-url|randompage ** formatnotes | Format Notes ** helppage|help * SEARCH * TOOLBO...")
- 18:06, 27 July 2014 (diff | hist) . . (+52) . . Main Page (→Special functions)
- 08:02, 27 July 2014 (diff | hist) . . (+284) . . Main Page (→Special functions)
- 07:58, 27 July 2014 (diff | hist) . . (+176) . . Main Page (→Special functions)
- 07:56, 27 July 2014 (diff | hist) . . (-1) . . Partition
- 07:55, 27 July 2014 (diff | hist) . . (+374) . . N Partition (Created page with "Let $n$ be an integer. Let $p(0)=1$ and let $p(n)=0$ for negative $n$. For positive $n$, the partition function $p(n)$ is the number of possible partitions of a number $n$ int...")
- 07:52, 27 July 2014 (diff | hist) . . (+63) . . Main Page (→Special functions)
- 07:51, 27 July 2014 (diff | hist) . . (+27) . . Main Page (→Special functions)
- 07:51, 27 July 2014 (diff | hist) . . (+44) . . Main Page (→Special functions)
- 07:34, 27 July 2014 (diff | hist) . . (+20) . . Main Page (→Special functions)
- 07:33, 27 July 2014 (diff | hist) . . (+27) . . Main Page (→Special functions)
- 07:32, 27 July 2014 (diff | hist) . . (+26) . . Main Page (→Special functions)
- 07:32, 27 July 2014 (diff | hist) . . (+275) . . Sine (→Properties)
- 07:31, 27 July 2014 (diff | hist) . . (+419) . . N Sine (Created page with "The sine function, usually written $\sin$, is the solution of the second order initial value problem $y''=-y;y(0)=0$. =Properties= <div class="toccolours mw-collapsible mw-co...")
- 07:27, 27 July 2014 (diff | hist) . . (-1) . . Error function
- 07:27, 27 July 2014 (diff | hist) . . (+81) . . N Error function (Created page with "$$\mathrm{erf}(x)=\dfrac{2}{\sqrt{\pi}}\displaystyle\int_0^x e^{-\tau^2} d\tau.$$")
- 07:26, 27 July 2014 (diff | hist) . . (+25) . . Main Page (→Special functions)
- 07:26, 27 July 2014 (diff | hist) . . (+537) . . Gamma
- 07:24, 27 July 2014 (diff | hist) . . (-10) . . Main Page (→Special functions)
- 07:22, 27 July 2014 (diff | hist) . . (+1,473) . . Q-Gamma
- 07:12, 27 July 2014 (diff | hist) . . (+144) . . Q-Pochhammer
- 07:08, 27 July 2014 (diff | hist) . . (+273) . . N Q-Gamma (Created page with "Let $0<q<1$. Define $$\Gamma_q(x) = \dfrac{(q;q)_{\infty}}{(q^x;q)_{\infty}}(1-q)^{1-x},$$ where $(\cdot;\cdot)_{\infty}$ denotes the q-Pochhammer symbol. =References= As...")
- 07:05, 27 July 2014 (diff | hist) . . (+74) . . Q-Pochhammer
- 07:02, 27 July 2014 (diff | hist) . . (+6) . . Main Page (→Special functions)
- 07:02, 27 July 2014 (diff | hist) . . (+110) . . Main Page (→Special functions)
- 06:12, 27 July 2014 (diff | hist) . . (+52) . . Main Page (→Special functions)
- 05:15, 27 July 2014 (diff | hist) . . (+1,386) . . Gamma
- 05:06, 27 July 2014 (diff | hist) . . (+24) . . Main Page (→Special functions)
- 05:03, 27 July 2014 (diff | hist) . . (+17) . . Main Page (→Special functions)
- 05:03, 27 July 2014 (diff | hist) . . (+39) . . Main Page (→Special functions)
- 04:24, 27 July 2014 (diff | hist) . . (+123) . . Riemann zeta
- 04:08, 27 July 2014 (diff | hist) . . (+198) . . N Dirichlet eta (Created page with "Let $\mathrm{Re} \hspace{2pt} z > 0$, then define $$\eta(z) = \displaystyle\sum_{n=1}^{\infty} \dfrac{(-1)^{n-1}}{n^s}.$$ This series is clearly the Riemann zeta function...")
- 04:06, 27 July 2014 (diff | hist) . . (+33) . . Main Page (→Special functions)
- 04:05, 27 July 2014 (diff | hist) . . (+152) . . N Dedekind eta (Created page with "Let $q=e^{2\pi i t}$. We define the Dedekind eta function by the formula $$\eta(t) = e^{\frac{\pi i t}{12}} \displaystyle\prod_{n=1}^{\infty} (1-q^n).$$")
- 04:01, 27 July 2014 (diff | hist) . . (+32) . . Main Page (→Special functions)
- 06:55, 24 July 2014 (diff | hist) . . (-2) . . Specialfunctionswiki:About
- 06:54, 24 July 2014 (diff | hist) . . (+63) . . N Specialfunctionswiki:About (Created page with "This wiki is maintained by [http://tomcuchta.com | Tom Cuchta].")
- 06:53, 24 July 2014 (diff | hist) . . (+7) . . Main Page (→Special functions)
- 01:29, 23 July 2014 (diff | hist) . . (+115) . . N Q-Pochhammer (Created page with "$$(a;q)_n=\displaystyle\prod_{j=0}^{n-1} (1-aq^k)$$ $$(a;q)_{\infty} = \displaystyle\prod_{j=0}^{\infty} (1-aq^k)$$")
- 22:06, 22 July 2014 (diff | hist) . . (+30) . . Main Page (→Special functions)
- 00:04, 22 July 2014 (diff | hist) . . (+6) . . Main Page (→Special functions)
- 19:51, 21 July 2014 (diff | hist) . . (+28) . . Main Page (→Special functions)
- 19:50, 21 July 2014 (diff | hist) . . (+89) . . Main Page (→Special functions)
- 21:43, 20 July 2014 (diff | hist) . . (+158) . . N Gamma (Created page with "The gamma function is the function defined by the integral (initially for positive values of $x$) $$\Gamma(x)=\displaystyle\int_0^{\infty} x^{t-1}e^{-x} dx.$$")
- 21:41, 20 July 2014 (diff | hist) . . (+6) . . Main Page (→Special functions)
- 21:41, 20 July 2014 (diff | hist) . . (-25) . . Main Page (→Special functions)
- 19:01, 18 July 2014 (diff | hist) . . (+9) . . Main Page (→Special functions)
- 19:00, 18 July 2014 (diff | hist) . . (0) . . m Riemann zeta (Tom moved page Riemann zeta to Riemann zeta function)
- 00:24, 15 July 2014 (diff | hist) . . (+16) . . Riemann zeta
- 00:23, 15 July 2014 (diff | hist) . . (+382) . . N Riemann zeta (Created page with "Consider the function $\zeta$ defined by the series $$\zeta(z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{n^z}.$$ <div class="toccolours mw-collapsible mw-collapsed" style=...")
- 00:18, 15 July 2014 (diff | hist) . . (+47) . . Main Page (→Special functions)
- 23:07, 14 July 2014 (diff | hist) . . (-25) . . Main Page (→Other)
- 23:00, 14 July 2014 (diff | hist) . . (+250) . . Main Page
- 22:57, 14 July 2014 (diff | hist) . . (-1,361) . . m Main Page (Reverted edits by Yulissa022 (talk) to last revision by Tom)
- 22:25, 14 July 2014 (diff | hist) . . (-1,023) . . m Main Page (Reverted edits by MagdaleBarrios (talk) to last revision by Tom)
- 22:13, 14 July 2014 (diff | hist) . . (+292) . . m Main Page (Reverted edits by Jamila11Ybobcy (talk) to last revision by Tom)
- 10:30, 4 July 2014 (diff | hist) . . (+1,868) . . Hypergeometric pFq (→Derivatives)
- 06:46, 4 July 2014 (diff | hist) . . (+920) . . Hypergeometric pFq (→Case I: $p<q+1$)
- 06:35, 4 July 2014 (diff | hist) . . (+57) . . Hypergeometric pFq
- 06:05, 4 July 2014 (diff | hist) . . (+4) . . Hypergeometric pFq (→Differential equation)
- 05:53, 4 July 2014 (diff | hist) . . (-4) . . Hypergeometric pFq (→Derivatives)
- 05:52, 4 July 2014 (diff | hist) . . (+7) . . Hypergeometric pFq (→Derivatives)
- 05:41, 4 July 2014 (diff | hist) . . (+36) . . Hypergeometric pFq
- 05:27, 4 July 2014 (diff | hist) . . (-9) . . Hypergeometric pFq (→Derivatives)
- 05:27, 4 July 2014 (diff | hist) . . (+817) . . Hypergeometric pFq (→Derivatives)
- 03:35, 4 July 2014 (diff | hist) . . (+374) . . Hypergeometric pFq
- 03:24, 4 July 2014 (diff | hist) . . (+497) . . Hypergeometric pFq
- 03:18, 4 July 2014 (diff | hist) . . (-351) . . Hypergeometric pFq (→Differential equation)
- 01:39, 4 July 2014 (diff | hist) . . (+68) . . Hypergeometric pFq (→Differential equation)
- 01:38, 4 July 2014 (diff | hist) . . (+430) . . Hypergeometric pFq
- 01:10, 4 July 2014 (diff | hist) . . (+5) . . Main Page
- 01:10, 4 July 2014 (diff | hist) . . (+1) . . Main Page
- 01:10, 4 July 2014 (diff | hist) . . (+218) . . Main Page
- 23:07, 3 July 2014 (diff | hist) . . (+42) . . Main Page (→Special functions)
- 22:49, 3 July 2014 (diff | hist) . . (-1) . . Hypergeometric pFq
- 22:49, 3 July 2014 (diff | hist) . . (+62) . . Hypergeometric pFq
- 22:13, 3 July 2014 (diff | hist) . . (+28) . . Ratio test
- 21:10, 3 July 2014 (diff | hist) . . (-58) . . Main Page
- 15:51, 3 July 2014 (diff | hist) . . (+3,230) . . Hypergeometric pFq
- 06:26, 3 July 2014 (diff | hist) . . (+430) . . N Ratio test (Created page with "Let $\{a_1,a_2,\ldots\} \subset \mathbb{C}$ and consider the infinite series $\displaystyle\sum_{k=0}^{\infty} a_k.$ Define $$L=\displaystyle\lim_{k \rightarrow \infty} \left|...")
- 05:47, 3 July 2014 (diff | hist) . . (+35) . . Main Page
- 05:44, 3 July 2014 (diff | hist) . . (+7) . . Main Page
- 05:44, 3 July 2014 (diff | hist) . . (+88) . . Main Page
- 05:43, 3 July 2014 (diff | hist) . . (+1,117) . . N Hypergeometric pFq (Created page with "Let $p,q \in \{0,1,2,\ldots\}$ and $a_j,b_{\ell} \in \mathbb{R}$ for $j=1,\ldots,p$ and $\ell=1,\ldots,q$. Define the generalized hypergeometric function $${}_pF_q(a_1,a_2,\ld...")
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