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)},$$ where $\Omega(n)$ indicates the number of prime factors of $n$, counted with multiplicity....")
- 16:13, 4 October 2014 (diff | hist) . . (+1) . . Mertens function (current)
- 16:13, 4 October 2014 (diff | hist) . . (+996) . . Möbius
- 16:13, 4 October 2014 (diff | hist) . . (0) . . m Möbius (Tom moved page Mobius function to Möbius function)
- 16:13, 4 October 2014 (diff | hist) . . (+30) . . N Mobius function (Tom moved page Mobius function to Möbius function) (current)
- 16:11, 4 October 2014 (diff | hist) . . (+1) . . N Möbius (Created page with "a")
- 16:11, 4 October 2014 (diff | hist) . . (+128) . . N Mertens function (Created page with "Merten's function is defined by the formula $$M(n) = \displaystyle\sum_{k=1}^n \mu(k),$$ where $\mu$ is the Mobius function.")
- 16:10, 4 October 2014 (diff | hist) . . (+55) . . Main Page (→Special functions in number theory)
- 16:10, 4 October 2014 (diff | hist) . . (+27) . . Main Page (→Special functions in number theory)
- 16:09, 4 October 2014 (diff | hist) . . (+38) . . Main Page
- 16:01, 4 October 2014 (diff | hist) . . (+27) . . Main Page (→Special functions)
- 16:00, 4 October 2014 (diff | hist) . . (+525) . . Euler totient
- 15:58, 4 October 2014 (diff | hist) . . (+399) . . Euler totient
- 15:56, 4 October 2014 (diff | hist) . . (+185) . . N Euler totient (Created page with "Euler's totient function (sometimes called Euler's $\phi$ function) is the function <br /> <center>$\phi(n) =$ # of positive integers $\leq n$ that are relatively prime to $n$...")
- 15:53, 4 October 2014 (diff | hist) . . (0) . . m Tangent (Tom moved page Tangent function to Tangent)
- 15:53, 4 October 2014 (diff | hist) . . (+21) . . N Tangent function (Tom moved page Tangent function to Tangent) (current)
- 15:53, 4 October 2014 (diff | hist) . . (+29) . . Main Page
- 15:52, 4 October 2014 (diff | hist) . . (0) . . m Cosine (Tom moved page Cosine function to Cosine)
- 15:52, 4 October 2014 (diff | hist) . . (+20) . . N Cosine function (Tom moved page Cosine function to Cosine) (current)
- 15:52, 4 October 2014 (diff | hist) . . (0) . . m Sine (Tom moved page Sine function to Sine)
- 15:52, 4 October 2014 (diff | hist) . . (+18) . . N Sine function (Tom moved page Sine function to Sine) (current)
- 15:51, 4 October 2014 (diff | hist) . . (+126) . . N Tangent (Created page with "The tangent function is defined as the ratio of the sine and cosine functions: $$\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
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