User contributions
(newest | oldest) View (newer 50 | older 50) (20 | 50 | 100 | 250 | 500)
- 03:47, 28 March 2017 (diff | hist) . . (+20) . . Main Page (→Depreciated trigonometric functions)
- 03:47, 28 March 2017 (diff | hist) . . (+221) . . N Covercosine (Created page with "The coversine function $\mathrm{coversin} \colon \mathbb{C} \rightarrow \mathbb{C}$ defined by $$\mathrm{coversin}(z) = 1-\sin(z),$$ where $\sin$ denotes sine. =Propertie...") (current)
- 03:45, 28 March 2017 (diff | hist) . . (+33) . . Havercosine
- 03:45, 28 March 2017 (diff | hist) . . (-25) . . Haversine (current)
- 03:45, 28 March 2017 (diff | hist) . . (+216) . . N Havercosine (Created page with "The havercosine function $\mathrm{havercos} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by $$\mathrm{havercos}(\theta) = \dfrac{1+\cos(\theta)}{2}.$$ =Properties= =...")
- 03:41, 28 March 2017 (diff | hist) . . (0) . . Error function is odd (→Proof) (current)
- 03:41, 28 March 2017 (diff | hist) . . (-43) . . Error function is odd
- 03:41, 28 March 2017 (diff | hist) . . (+432) . . Error function is odd (→Proof)
- 20:15, 25 March 2017 (diff | hist) . . (+14) . . Pell constant (current)
- 15:31, 18 March 2017 (diff | hist) . . (-13) . . Riemann xi (current)
- 15:31, 18 March 2017 (diff | hist) . . (+10) . . Riemann xi
- 15:29, 18 March 2017 (diff | hist) . . (+268) . . N Riemann-Landau xi is even (Created page with "==Theorem== Riemann-Landau xi is an even function. ==Proof== ==References== * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Rieman...") (current)
- 15:28, 18 March 2017 (diff | hist) . . (+403) . . N Riemann-Landau xi (Created page with "The Riemann-Landau $\Xi$ function is defined by $$\Xi(z) = \xi \left( \dfrac{1}{2} + iz \right),$$ where $\xi$ denotes Riemann xi. =Properties= Riemann-Landau xi is eve...") (current)
- 15:27, 18 March 2017 (diff | hist) . . (+17) . . Functional equation for Riemann xi (→References) (current)
- 15:25, 18 March 2017 (diff | hist) . . (+28) . . Main Page (→Special functions)
- 15:23, 18 March 2017 (diff | hist) . . (+72) . . Book:Edward Charles Titchmarsh/The Zeta-Function of Riemann (current)
- 15:20, 18 March 2017 (diff | hist) . . (+295) . . N Functional equation for Riemann xi (Created page with "==Theorem== The following formula holds: $$\xi(z)=\xi(1-z),$$ where $\xi$ denotes Riemann xi. ==Proof== ==References== * {{BookReference|The Zeta-Function of Riemann|193...")
- 15:19, 18 March 2017 (diff | hist) . . (-594) . . Riemann xi
- 15:18, 18 March 2017 (diff | hist) . . (+4) . . Functional equation for Riemann zeta with cosine (→References) (current)
- 00:02, 18 March 2017 (diff | hist) . . (+111) . . Book:Edward Charles Titchmarsh/The Zeta-Function of Riemann (→Contents)
- 00:01, 18 March 2017 (diff | hist) . . (+504) . . N Functional equation for Riemann zeta with cosine (Created page with "==Theorem== The following formula holds for all $z \in \mathbb{C}$: $$\zeta(1-z)=2^{1-z} \pi^{-z} \cos \left( \dfrac{\pi z}{2} \right)\Gamma(z)\zeta(z),$$ where $\zeta$ denote...")
- 00:00, 18 March 2017 (diff | hist) . . (+536) . . N Functional equation for Riemann zeta (Created page with "==Theorem== The following formula holds for all $z \in \mathbb{C}$: $$\zeta(z)=2^z \pi^{z-1} \sin \left( \dfrac{\pi z}{2} \right) \Gamma(1-z)\zeta(1-z),$$ where $\zeta$ denote...") (current)
- 23:57, 17 March 2017 (diff | hist) . . (+30) . . Riemann zeta at even integers (→References) (current)
- 23:56, 17 March 2017 (diff | hist) . . (+106) . . Riemann zeta (→Properties)
- 23:54, 17 March 2017 (diff | hist) . . (+1) . . Book:Edward Charles Titchmarsh/The Zeta-Function of Riemann (→Contents)
- 23:53, 17 March 2017 (diff | hist) . . (+5) . . Riemann zeta (→Properties)
- 23:45, 17 March 2017 (diff | hist) . . (+42) . . Book:Edward Charles Titchmarsh/The Zeta-Function of Riemann (→Contents)
- 23:45, 17 March 2017 (diff | hist) . . (+544) . . N Riemann zeta at even integers (Created page with "==Theorem== The following formula holds for even integers $n$ and $m \in \{1,2,3,\ldots\}$: $$\zeta(n)= \left\{ \begin{array}{ll} 0 &, \quad n=-2m, \\ -\dfrac{1}{2} &, \quad n...")
- 23:42, 17 March 2017 (diff | hist) . . (+5) . . Riemann zeta as contour integral (→References) (current)
- 23:40, 17 March 2017 (diff | hist) . . (+18) . . Riemann zeta as contour integral (→References)
- 23:40, 17 March 2017 (diff | hist) . . (+35) . . Riemann zeta (→Properties)
- 23:39, 17 March 2017 (diff | hist) . . (+45) . . Book:Edward Charles Titchmarsh/The Zeta-Function of Riemann
- 23:38, 17 March 2017 (diff | hist) . . (+26) . . Riemann zeta as integral of monomial divided by an exponential (current)
- 23:38, 17 March 2017 (diff | hist) . . (+741) . . N Riemann zeta as contour integral (Created page with "==Theorem== The following formula holds: $$\zeta(z)=-\dfrac{\Gamma(1-z)}{2\pi i} \displaystyle\int_C \dfrac{(-\xi)^{z-1}}{e^{\xi}-1} \mathrm{d}\xi,$$ where $\zeta$ is Rieman...")
- 23:29, 17 March 2017 (diff | hist) . . (+16) . . Prime zeta P (→Videos) (current)
- 23:27, 17 March 2017 (diff | hist) . . (+24) . . Dirichlet series (current)
- 23:27, 17 March 2017 (diff | hist) . . (+74) . . Book:G.H. Hardy/The General Theory Of Dirichlet's Series (→Contents) (current)
- 23:16, 17 March 2017 (diff | hist) . . (+2) . . Dirichlet series
- 23:16, 17 March 2017 (diff | hist) . . (+2) . . General Dirichlet series (→References) (current)
- 23:15, 17 March 2017 (diff | hist) . . (-3) . . Dirichlet series
- 23:15, 17 March 2017 (diff | hist) . . (+577) . . N General Dirichlet series (Created page with "__NOTOC__ Let $z \in \mathbb{C}$ and let $\lambda_k \in \mathbb{R}$ for $k \in \{0,1,2\ldots\}$ be so that $\lambda_{k} < \lambda_{k+1}$ and $\displaystyle\lim_{k \rightarrow...")
- 23:10, 17 March 2017 (diff | hist) . . (+395) . . N Dirichlet series (Created page with "Let $z \in \mathbb{C}$. A Dirichlet series is a series of the form $$\displaystyle\sum_{k=1}^{\infty} \dfrac{a_k}{k^z}.$$ ==Properties== ==References== {{BookReference|T...")
- 22:59, 17 March 2017 (diff | hist) . . (+43) . . Riemann zeta (→Properties)
- 22:56, 17 March 2017 (diff | hist) . . (+61) . . Book:Milton Abramowitz/Handbook of mathematical functions
- 22:55, 17 March 2017 (diff | hist) . . (+79) . . Series for polygamma in terms of Riemann zeta (current)
- 22:51, 17 March 2017 (diff | hist) . . (+380) . . N Series for polygamma in terms of Riemann zeta (Created page with "==Theorem== The following formula holds for $|z|<1$: $$\psi^{(n)}(z+1)=(-1)^{n+1} \displaystyle\sum_{k=n}^{\infty} k! (-1)^{k+1}\zeta(k+1)z^{k-n}.$$ ==Proof== ==References==...")
- 22:51, 17 March 2017 (diff | hist) . . (+39) . . Polygamma multiplication formula (→References) (current)
- 22:47, 17 March 2017 (diff | hist) . . (+56) . . Polygamma (→Properties) (current)
- 22:46, 17 March 2017 (diff | hist) . . (+2) . . Polygamma multiplication formula (→References)
- 22:46, 17 March 2017 (diff | hist) . . (+2) . . Polygamma reflection formula (→References) (current)
(newest | oldest) View (newer 50 | older 50) (20 | 50 | 100 | 250 | 500)
