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- 07:40, 19 March 2024 Integration by Parts/Riemann-Stieltjes Integral (hist | edit) [6,326 bytes] CircuitCraft (talk | contribs) (Created page with "== Theorem == Let $f, \alpha$ be a real functions that are bounded on $\closedint a b$. Suppose that $f$ is Riemann-Stieltjes integrable with respect to $\alpha$ on $\closedint a b$. Then, $\alpha$ is Riemann-Stieltjes integrable with respect to $f$ on $\closedint a b$ and: :$\ds \int_a^b f \rd \alpha + \int_a^b...")
- 06:04, 19 March 2024 Linear Combination of Riemann-Stieltjes Integrals/Integrator (hist | edit) [4,072 bytes] CircuitCraft (talk | contribs) (Created page with "== Theorem == Let $f, \alpha, \beta$ be a real functions that are bounded on $\closedint a b$. Let $c_1, c_2 \in \R$. Suppose that $f$ is Riemann-Stieltjes integrable with respect both $\alpha$ and $\beta$ on $\closedint a b$ and: :$\ds \int_a^b f \rd \alpha = A$ :$\ds \int_a^b f \rd \beta = B$ Then, $f$ is Definition:Riemann-Stieltjes Integral|Rieman...")
- 05:37, 19 March 2024 Linear Combination of Riemann-Stieltjes Integrals/Integrand (hist | edit) [3,928 bytes] CircuitCraft (talk | contribs) (Created page with "== Theorem == Let $f, g, \alpha$ be a real functions that are bounded on $\closedint a b$. Let $c_1, c_2 \in \R$. Suppose that $f$ and $g$ are Riemann-Stieltjes integrable with respect to $\alpha$ on $\closedint a b$ and: :$\ds \int_a^b f \rd \alpha = A$ :$\ds \int_a^b g \rd \alpha = B$ Then, the real function $h : \closedin...")
- 23:18, 18 March 2024 Prime whose Divisor Sum is Square is 3 (hist | edit) [1,059 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == There is exactly $1$ prime number whose divisor sum is a square number, and that is $3$: :$\map {\sigma_1} 3 = 4$ == Proof == That $\map {\sigma_1} 3 = 4$ is shown at {{DSFLink|3}}. It remains to be shown there are no more. Let $n \in \N$ such that $\map {\sigma_1} n$ is square. :$\map {\sigma_1} n = m^2$ Suppose $n$ is Definit...")
- 20:38, 18 March 2024 Graphical Solution to Simultaneous Equations/Examples/Single Equation (hist | edit) [1,000 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Graphical Solution to Simultaneous Equations == <onlyinclude> It is possible to apply the technique of a '''graphical solution to simultaneous equations''' to a single equation by setting one of the simultaneous equations to $y = \map f x$, and the other to $y = 0$. </onlyinclude...")
- 20:31, 18 March 2024 Lagrange's Theorem (Number Theory)/Examples/Non-Prime Index (hist | edit) [368 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Use of Lagrange's Theorem (Number Theory) == <onlyinclude> {{WIP}} </onlyinclude> Category:Examples of Use of Lagrange's Theorem (Number Theory)")
- 20:30, 18 March 2024 Lagrange's Theorem (Number Theory)/Examples (hist | edit) [312 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Use of Lagrange's Theorem (Number Theory) == <onlyinclude> === Non-Prime Index === {{:Lagrange's Theorem (Number Theory)/Examples/Non-Prime Index}}</onlyinclude> Category:Examples of Use of Lagrange's Theorem (Number Theory)")
- 20:23, 18 March 2024 Graphical Solution to Simultaneous Equations/Examples (hist | edit) [396 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Graphical Solutions to Simultaneous Equations == <onlyinclude> === Single Equation === {{:Graphical Solution to Simultaneous Equations/Examples/Single Equation}}</onlyinclude> Category:Graphical Solutions to Simultaneous Equations")
- 12:33, 18 March 2024 Derivative of Composite Function/Also presented as (hist | edit) [3,211 bytes] Prime.mover (talk | contribs) (Created page with "== Derivative of Composite Function: Also presented as == <onlyinclude> The Derivative of Composite Function is also often seen presented using Leibniz's notation for derivatives: :$\dfrac {\d y} {\d x} = \dfrac {\d y} {\d u} \cdot \dfrac {\d u} {\d x}$ where: :$\dfrac {\d y} {\d x}$ is the derivative of $y$ with respect to $x$ :$\dfrac {\d y} {\d u}$ is the Definition:Derivative|deriv...")
- 10:38, 18 March 2024 Derivative of Composite Function/Also known as (hist | edit) [2,984 bytes] Prime.mover (talk | contribs) (Created page with "== Derivative of Composite Function: Also known as == <onlyinclude> The rule to calculate the '''Derivative of Composite Function''' is often informally referred to as: :the '''Chain Rule for Derivatives''' :the '''Chain Rule for Differentiation'' Some sources refer to it as just the '''Chain Rule''', but the latter term has a number of applications. </onlyinclude> == Sources == {{SourceReview}} * {{BookReference|A Note Book in Pure Mathematics|1...")
- 10:27, 18 March 2024 Derivative of Composite Function/Proof 2 (hist | edit) [2,204 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Derivative of Composite Function}} == Proof == <onlyinclude> Let $\map g x = y$, and let: {{begin-eqn}} {{eqn | l = \map g {x + \delta x} | r = y + \delta y | c = }} {{eqn | ll= \leadsto | l = \delta y | r = \map g {x + \delta x} - \map g x | c = }} {{end-eqn}} Thus: :$\delta y \to 0$ as $\delta x \to 0$ and: :$(1): \quad \dfrac {\delta y} {\delta x} \to \map {g'} x$ There are two cases to consider: === Case 1 ===...")
- 10:24, 18 March 2024 Derivative of Composite Function/Proof 1 (hist | edit) [2,863 bytes] Prime.mover (talk | contribs) (Created page with "{{Previous POTW|1 December 2008|14 December 2008}} == Theorem == {{:Derivative of Composite Function}} == Proof == <onlyinclude> Let $f, g, x_0$ satisfy the conditions of the theorem. Define $g^* : I \to \R$ as: :$\map {g^*} x = \begin{cases} \dfrac {\map g x - \map g {x_0}} {x - x_0} & : x \ne x_0 \\ \map {g'} {x_0} & : x = x_0 \end{cases}$ Then, for every $x \in I$: :$\paren 1: \quad \map g x - \map g {x_0} = \paren {x - x_0} \map {g^*} x$ for when $x = x_0$, both...")
- 02:21, 18 March 2024 Sobolev Norm is Norm (hist | edit) [2,563 bytes] Hbghlyj (talk | contribs) (Created page with "== Theorem == Let $k \in \Z_+$ and $1 \le p \le \infty$. Let $U \subset \R^n$ be an open set. Then the Sobolev norm is a norm on the Sobolev space $\map{W^{k,p}} U$. == Proof == === Property $(\text N 1)$ === === Property $(\text N 2)$ === === Property $(\text N 3)$ === Assume $u, v \in \map {W^{k,p}} U$. If $1\le...")
- 01:47, 18 March 2024 Sobolev Space is Banach Space (hist | edit) [1,982 bytes] Hbghlyj (talk | contribs) (Created page with "== Theorem == The Sobolev space $\map {H^n} {a, b}$ equipped with the Sobolev norm is a Definition:Banach Space. == Proof == {{ProofWanted}} == Sources == * {{BookReference|Partial Differential Equations|2010|Lawrence Craig Evans}} Theorem 2 (Sobolev spaces as function spaces). Category:Definitions/Functional Analysis Category:Category:Banach Spaces")
- 23:00, 17 March 2024 Thomsen Graph is not Planar (hist | edit) [2,821 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == The complete bipartite graph $K_{3, 3}$ is not planar. == Proof == {{ProofWanted}} == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Complete Graph K5 is not Planar|next = Definition:Graphical Solution to Simultaneous Equations|entry = graph|index = 2}} * {{BookReference|The Penguin Dictionary of Mathematic...") originally created as "Complete Bipartite Graph K3,3 is not Planar"
- 22:49, 17 March 2024 Complete Graph K5 is not Planar (hist | edit) [2,095 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == The complete graph $K_5$ is not planar. == Proof == {{ProofWanted}} == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Planar Graph/Examples/Complete Bipartite Graph K2,3|next = Complete Bipartite Graph K3,3 is not Planar|entry = graph|index = 2}} * {{BookReference|The Penguin Dictionary of Mathematics|2008|David Nels...")
- 22:30, 17 March 2024 Planar Graph/Examples/Complete Bipartite Graph K2,3 (hist | edit) [737 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Planar Graph == <onlyinclude> The '''complete bipartite graph''' $K_{2, 3}$ is a '''planar graph''': :220px </onlyinclude> Category:Examples of Planar Graphs")
- 22:17, 17 March 2024 Planar Graph/Examples/Arbitrary Example 1 (hist | edit) [217 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Planar Graph == <onlyinclude> This is a '''planar graph''': :300px </onlyinclude> Category:Examples of Planar Graphs")
- 22:11, 17 March 2024 Planar Graph/Examples (hist | edit) [398 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Planar Graphs == <onlyinclude> === Arbitrary Example === {{:Planar Graph/Examples/Arbitrary Example 1}} === Complete Bipartite Graph K2,3 === {{:Planar Graph/Examples/Complete Bipartite Graph K2,3}}</onlyinclude> Category:Examples of Planar Graphs")
- 22:02, 17 March 2024 Complete Graph is Regular/Examples/K5 (hist | edit) [705 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Use of Complete Graph is Regular == <onlyinclude> The '''complete graph''' $K_5$ of order $5$ is $4$-regular. </onlyinclude> == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Definition:Regular Graph|next = Definition:Bipartite Graph|entry = graph|index = 2}} * {{BookReference|The Pengu...")
- 21:57, 17 March 2024 Complete Graph is Regular/Examples (hist | edit) [255 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Use of Complete Graph is Regular == <onlyinclude> === Complete Graph $K_5$ === {{:Complete Graph is Regular/Examples/K5}}</onlyinclude> Category:Examples of Use of Complete Graph is Regular")
- 18:14, 17 March 2024 Kernel of Linear Transformation is Linear Subspace (hist | edit) [1,345 bytes] Hbghlyj (talk | contribs) (Created page with "== Theorem == Let $V, W$ be normed vector spaces on a field $F$. Let $T: V \to W$ be a bounded linear transformation. Then $\ker T$, the kernel of $T$, is a linear subspace of $V$. == Proof == By Kernel of Linear Transformation contains Zero Vector, $0_V \in \ker T$. =...")
- 16:35, 17 March 2024 Graph Paper/Examples/Semilogarithmic (hist | edit) [859 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Semilogarithmic Graph Paper == <onlyinclude> This is an example of '''graph paper''' that can be used for presenting graphs of functions of the form $y = a^x$: :600px </onlyinclude> Category:Examples of Graph Paper")
- 16:35, 17 March 2024 Graph Paper/Examples/Logarithmic (hist | edit) [900 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Logarithmic Graph Paper == <onlyinclude> This is an example of '''graph paper''' that can be used for presenting graphs of functions of the form $y = a x^n$: :600px </onlyinclude> Category:Examples of Graph Paper")
- 15:49, 17 March 2024 Graph Paper/Examples/Polar (hist | edit) [359 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Graph Paper == <onlyinclude> This is an example of the sort of '''graph paper''' that would be used for presenting graphs on a polar plane: :600px </onlyinclude> Category:Examples of Graph Paper")
- 15:45, 17 March 2024 Graph Paper/Examples/Cartesian (hist | edit) [352 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Graph Paper == <onlyinclude> This is an example of the conventional '''graph paper''' used for presenting graphs on a Cartesian plane: :600px </onlyinclude> Category:Examples of Graph Paper")
- 15:30, 17 March 2024 Isomorphism between Group of Units of Ring of Integers Modulo p^n and C((p-1)p^(n-1)) (hist | edit) [891 bytes] Hbghlyj (talk | contribs) (Created page with "== Theorem == Let $n \in \Z_{\ge 0}$ be a positive integer and $n \ge 2$. Let $p$ be an odd prime. Let $R = \struct {\Z / p^n \Z, +, \times}$ be the ring of integers modulo $2^n$. Let $U = \struct {\paren {\Z / p^n \Z}^\times, \times}$ denote the group of units of $R$. Let $C_{(p - 1)p^{n - 1}}$ be be...")
- 14:44, 17 March 2024 Graph Paper/Examples (hist | edit) [493 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Graph Paper == <onlyinclude> === Cartesian === {{:Graph Paper/Examples/Cartesian}} === Polar === {{:Graph Paper/Examples/Polar}} === Logarithmic === {{:Graph Paper/Examples/Logarithmic}} === Semilogarithmic === {{:Graph Paper/Examples/Semilogarithmic}}</onlyinclude> Category:Example...")
- 13:42, 17 March 2024 Order of 5 in Units of Ring of Integers Modulo 2^n (hist | edit) [600 bytes] Hbghlyj (talk | contribs) (Created page with "== Theorem == Let $n \in \Z_{\ge 0}$ be a positive integer and $n \ge 2$. Let $\struct {\Z / 2^n \Z, +, \times}$ be the ring of integers modulo ^n$. Let $U = \struct {\paren {\Z / 2^n \Z}^\times, \times}$ denote the group of units of $\struct {\Z / 2^n \Z, +, \times}$. The order of $5$ in $U$ is $2^{n-2}$. == Proof == {{Pro...")
- 09:55, 17 March 2024 Radical of Integer/Sequence (hist | edit) [1,660 bytes] Prime.mover (talk | contribs) (Created page with "== Sequence of Radicals of Integers == <onlyinclude> The '''sequence of radicals''' of the integers beings: {{begin-table|wikitable = y|title = Radical of Integer}} {{Row-start}} {{Col-head|$n$}} {{Col-head|Decomposition}} {{Col-head|$\map \Rad n$}} |- |align="right" | $1$ |align="...")
- 22:03, 16 March 2024 Abel-Plana Formula (hist | edit) [1,258 bytes] Robkahn131 (talk | contribs) (Created page with "== Theorem == Let $\map f z$ be analytic for real part of $\map \Re z \ge 0$ and suppose that either :$\ds \sum_{n \mathop = 0}^{\infty} \map f n$ converges or $\ds \int_0^{\infty} \map f x \rd x $ converges. Assume further that :$\ds \lim_{y \mathop \to \infty} \size {\map f {x \pm i y} } e^{-2 \pi y} = 0$ uniformly in x on every Definitio...")
- 18:38, 16 March 2024 Lüroth's Theorem (hist | edit) [914 bytes] Hbghlyj (talk | contribs) (Created page with " == Theorem == Let \(K\) be a field and \(M\) be an intermediate field between \(K\) and \(\map K X\), for some indeterminate $X$. Then there exists a rational function \(\map f X\in \map K X\) such that :\(M=K(\map f X)\). In other words, every intermediate extension between \(K\) and \(\map K X\) is a Definition:Simp...") originally created as "Luroth's Theorem"
- 17:46, 16 March 2024 Gram-Schmidt Orthogonalization/Also known as (hist | edit) [882 bytes] Prime.mover (talk | contribs) (Created page with "== Gram-Schmidt Orthogonalization: Also known as == <onlyinclude> '''Gram-Schmidt Orthogonalization''' is known in some texts as '''Gram-Schmidt Orthonormalization'''. Some texts refer to this theorem as the '''Gram-Schmidt Orthogonalization Process'''. Some others use the term '''Gram-Schmidt Method'''. </onlyinclude> == Sources == {{SourceReview}} Category:Gram-Schmidt Orthogonalization")
- 17:12, 16 March 2024 Graeco-Latin Square/Examples/Order 3 (hist | edit) [874 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Graeco-Latin Square == <onlyinclude> The following is an example of a '''Graeco-Latin square''' of order $3$: $\begin{array} {|c|c|c|} \hline A \alpha & B \beta & C \gamma \\ \hline B \gamma & C \alpha & A \beta \\ \hline C \beta & A \gamma & B \alpha \\ \hline \end{array}$ </onlyinclude> == Sources == * {{BookReference|The Penguin Dictionary of...")
- 17:06, 16 March 2024 Graeco-Latin Square/Examples (hist | edit) [249 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Graeco-Latin Squares == <onlyinclude> === Order $ === {{:Graeco-Latin Square/Examples/Order 3}}</onlyinclude> Category:Examples of Graeco-Latin Squares")
- 15:46, 16 March 2024 Dirichlet's Integral Form of Digamma Function (hist | edit) [2,877 bytes] Robkahn131 (talk | contribs) (Created page with "== Theorem == Let $z$ be a complex number with a positive real part. Then: :$\ds \map \psi z = \int_0^\infty \paren {\frac {e^{-t} } t - \frac 1 {t \paren {1 + t}^z } } \rd t$ where $\psi$ is the digamma function. == Proof == We have: {{begin-eqn}} {{eqn | l = \map \psi z | r = \int_0^\infty \paren {\frac {e^{-t} } t - \frac {e^{-z...")
- 15:17, 16 March 2024 Slope/Examples/Arbitrary Example 1 (hist | edit) [1,220 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Slope == <onlyinclude> A '''slope''' or '''gradient''' of $1$ in $4$ indicates a vertical distance of $1$ unit for every $4$ units travelled along the road. This is also indicated as a ratio $1 : 4$ or a fraction $1 / 4$, or can also be expressed as the angle of...")
- 15:09, 16 March 2024 Slope/Examples (hist | edit) [209 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Slope == <onlyinclude> === Arbitrary Example === {{:Slope/Examples/Arbitrary Example 1}}</onlyinclude> Category:Examples of Slope")
- 12:23, 16 March 2024 Gordan's Theorem (hist | edit) [902 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> {{help|It's uncertain exactly what theorem is being referenced here in Nelson.}} </onlyinclude> == Proof == {{ProofWanted}} == Also known as == {{:Gordan's Theorem/Also known as}} {{Namedfor|Paul Albert Gordan|cat = Gordan}} == Historical Note == {{:Gordan's Theorem/Historical Note}} == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Ne...")
- 12:23, 16 March 2024 Gordan's Theorem/Also known as (hist | edit) [720 bytes] Prime.mover (talk | contribs) (Created page with "== Gordan's Theorem: Also known as == <onlyinclude> '''Gordan's Theorem''' is also known as the '''Finite Base Theorem'''. Some sources give the name '''Gordon's Theorem''', but that is incorrect. </onlyinclude> == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Gordan's Theorem/Historical Note|next = Gordan's Theorem|entry = Gordan, Paul Albert|subentry = 1837-1912}} * {{Boo...")
- 12:22, 16 March 2024 Gordan's Theorem/Historical Note (hist | edit) [818 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Gordan's Theorem == <onlyinclude> '''Gordan's Theorem''' was proved by {{AuthorRef|Paul Albert Gordan}} in $1868$. He tried to generalized it to higher-order forms, but was unsuccessful. {{AuthorRef|David Hilbert}} finally completed the work in $1888$. </onlyinclude> == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Mathematician:Paul Albert Gordan|next = Gorda...")
- 09:52, 16 March 2024 Ramaré's Theorem/Historical Note (hist | edit) [726 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Ramaré's Theorem == <onlyinclude> '''Ramaré's Theorem''' was proved by {{AuthorRef|Olivier Ramaré}} in $1995$. As such it makes inroads into the resolution of the Goldbach Conjecture. In $2014$ the result was strengthened by {{AuthorRef|Terence Tao}}, who reduced the number of primes to $5$. The name '''Ramaré's Theorem''' was coined by {{ProofWiki}} in order to refer to the result compactly. </only...")
- 09:45, 16 March 2024 Ramaré's Theorem (hist | edit) [663 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Every positive integer can be expressed as the sum of no more than $6$ prime numbers. == Proof == {{ProofWanted}} {{Namedfor|Olivier Ramaré|cat = Ramaré}} == Historical Note == {{:Ramaré's Theorem/Historical Note}} == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|2008|David Nelson|ed = 4th|edpage...")
- 09:35, 16 March 2024 Chen's Theorem/Historical Note (hist | edit) [682 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Chen's Theorem == <onlyinclude> '''Chen's Theorem''' was proved by {{AuthorRef|Chen Jingrun}} in $1973$. As such it made a major inroad into the resolution of Coldbach's Conjecture. </onlyinclude> == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Vinogradov's Theorem/Corollary 2|next = Chen's Theorem|entry = Goldbach's conjecture}} * {{BookReference|The Peng...")
- 09:09, 16 March 2024 Gödel's Incompleteness Theorems/Historical Note (hist | edit) [1,190 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Gödel's Incompleteness Theorems == <onlyinclude> '''Gödel's Incompleteness Theorems''' answered the second of Hilbert's $23$ (then) unsolved problems of mathematics. Hence it ended attempts, like those of {{AuthorRef|Alfred North Whitehead}} and {{AuthorRef|Bertrand Russell}}, to develop the whole of mathematics from a Definition:...")
- 17:22, 15 March 2024 Variance of Geometric Distribution/Formulation 2/Also presented as (hist | edit) [667 bytes] Prime.mover (talk | contribs) (Created page with "== Variance of Geometric Distribution: Formulation 2: Also presented as == <onlyinclude> The '''Variance of Geometric Distribution''' is also presented in the form: :$\var X = \dfrac q {p^2}$ where $q$ has been defined conventionally as $q = 1 - p$. </onlyinclude> == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|2008|David Nelson|ed = 4th|edpa...")
- 17:20, 15 March 2024 Expectation of Geometric Distribution/Formulation 2/Also presented as (hist | edit) [702 bytes] Prime.mover (talk | contribs) (Created page with "== Expectation of Geometric Distribution: Formulation 2: Also presented as == <onlyinclude> The '''Expectation of Geometric Distribution''' is also presented in the form: :$\var X = \dfrac q p$ where $q$ has been defined conventionally as $q = 1 - p$. </onlyinclude> == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|2008|David Nelson|ed =...")
- 17:03, 15 March 2024 Variance of Shifted Geometric Distribution/Also presented as (hist | edit) [588 bytes] Prime.mover (talk | contribs) (Created page with "== Variance of Shifted Geometric Distribution: Also known as == <onlyinclude> The '''Variance of Shifted Geometric Distribution''' is also presented in the form: :$\var X = \dfrac q {p^2}$ where $q$ has been defined conventionally as $q = 1 - p$. </onlyinclude> == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|2008|David Nelson|ed = 4th|edpage = Fourth Edition|prev = Variance of Shifted Geometric Distribution|next = Definition:Geometric Fig...")
- 16:04, 15 March 2024 Riemann-Hurwitz Formula/Also known as (hist | edit) [200 bytes] Prime.mover (talk | contribs) (Created page with "== Riemann-Hurwitz Formula: Also known as == <onlyinclude> The '''Riemann-Hurwitz Formula''' is also known as '''Hurwitz's Theorem'''. </onlyinclude> Category:Riemann-Hurwitz Formula")
- 16:04, 15 March 2024 Phi is 8 has only 5 solutions (hist | edit) [464 bytes] Hbghlyj (talk | contribs) (Created page with "==Theorem== $\map \phi n = 8$ has only 5 solutions: ==Proof== {{ProofWanted}}")