User contributions for Robkahn131
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23 April 2024
- 00:1700:17, 23 April 2024 diff hist −109 m Pi Squared is Irrational/Proof 1 No edit summary current
22 April 2024
- 23:4123:41, 22 April 2024 diff hist +1 m Fourier Cosine Coefficients for Even Function over Symmetric Range No edit summary
- 00:4000:40, 22 April 2024 diff hist +56 m Integral of Bounded Measurable Function with respect to Finite Signed Measure is Well-Defined added links current
- 00:3500:35, 22 April 2024 diff hist −229 m Pi is Irrational/Proof 2 No edit summary current
- 00:3400:34, 22 April 2024 diff hist +365 N Area under Arc of Sine Function Created page with "== Theorem == :$\ds \int_0^\pi \sin x \rd x = 2$ == Proof == {{begin-eqn}} {{eqn | l = \int_0^\pi \sin x \rd x | r = \bigintlimits {- \cos x} 0 \pi | c = Primitive of Sine Function }} {{eqn | r = 2 | c = Cosine of $\pi$, {{cos|0}} }} {{end-eqn}} {{qed}} Category:Definite Integrals involving Sine Function"
19 April 2024
- 18:5418:54, 19 April 2024 diff hist +1,315 m Pi is Irrational/Proof 2 No edit summary
- 18:5218:52, 19 April 2024 diff hist +6,014 N Pi is Irrational/Proof 2/Lemma Created page with "== Pi is Irrational: Lemma == <onlyinclude> Let $n \in \Z_{> 0}$ be a positive integer. Let it be supposed that $\pi$ is irrational, so that: :$\pi = \dfrac p q$ where $p$ and $q$ are integers and $q \ne 0$. Let $A_n$ be defined as: :$\ds A_n = \frac {q^n} {n!} \int_0^\pi \paren {x \paren {\pi - x} }^n \sin x \rd x$ Then: :$A_n = \paren {4 n - 2} q A_{n - 1} - p^2 A_{n - 2}$..."
- 18:3718:37, 19 April 2024 diff hist +56 m Equation of Catenary/Whewell No edit summary
- 18:2718:27, 19 April 2024 diff hist +2 m Pi Squared is Irrational/Proof 1 No edit summary
- 18:2218:22, 19 April 2024 diff hist +460 m Pi Squared is Irrational/Proof 1 No edit summary
- 04:3504:35, 19 April 2024 diff hist +50 m Pi is Irrational No edit summary
- 04:3304:33, 19 April 2024 diff hist +41 m Pi Squared is Irrational No edit summary
- 04:3004:30, 19 April 2024 diff hist −9 m Pi Squared is Irrational/Proof 1/Lemma No edit summary
- 04:2704:27, 19 April 2024 diff hist −4,346 Pi Squared is Irrational/Proof 1 No edit summary
- 04:2604:26, 19 April 2024 diff hist +5,216 N Pi Squared is Irrational/Proof 1/Lemma Created page with "== Pi Squared is Irrational/Proof 1: Lemma == <onlyinclude> Let $n \in \Z_{> 0}$ be a positive integer. Let $A_n$ be defined as: :$\ds A_n = \frac {q^n} {n!} \int_0^\pi \paren {x \paren {\pi - x} }^n \sin x \rd x$ Let $\pi^2 = \dfrac p q$ where $p$ and $q$ are integers and $q \ne 0$. Note that $\paren {q \pi}^2 = q^2 \paren {\dfrac p q} = p q$ is an integer. Then: :$A_n = \paren {4 n -..."
- 03:4203:42, 19 April 2024 diff hist 0 m Definite Integral from 0 to Pi of Sine of m x by Sine of n x No edit summary current
- 03:3503:35, 19 April 2024 diff hist 0 m Definite Integral from 0 to Pi of Sine of m x by Cosine of n x No edit summary current
- 03:3403:34, 19 April 2024 diff hist 0 m Integral to Infinity of Sine p x over x No edit summary current
- 03:3403:34, 19 April 2024 diff hist 0 m Integral to Infinity of Sine p x Sine q x over x Squared wasn't displaying correctly current
18 April 2024
- 00:3400:34, 18 April 2024 diff hist +4,628 m Pi Squared is Irrational/Proof 1 filled in a few clarifying details
16 April 2024
- 21:3921:39, 16 April 2024 diff hist +785 N Talk:Pi Squared is Irrational/Proof 2 Created page with "The proof has several errors - one is here: Let us define a polynomial: :$\ds \map f x = \frac {\paren {1 - x^2}^n} {n!} = \sum_{m \mathop = n}^{2 n} \frac {c_m} {n!} x^m$ for $c_m \in \Z$. If $n = 1$ {{begin-eqn}} {{eqn | l = \map f x | r = \frac {\paren {1 - x^2} } {1!} | c = $n = 1$ }} {{eqn | l = \sum_{m \mathop = n}^{2 n} \frac {c_m} {n!} x^m | r = \sum_{m \mathop = 1}^2 \frac {c_m} {1!} x^m | c = }} {{eqn | r = c_1 x + c_2 x^2 | c..."
12 April 2024
- 01:2801:28, 12 April 2024 diff hist +14,704 Solution to Hypergeometric Differential Equation No edit summary
10 April 2024
- 20:4320:43, 10 April 2024 diff hist +70 m ProofWiki:Potw No edit summary current
- 20:4320:43, 10 April 2024 diff hist +12 m Sum of nth Fibonacci Number over nth Power of 2/Proof 1 No edit summary
- 20:4320:43, 10 April 2024 diff hist +38 m Converting Decimal Expansion of Rational Number to Fraction No edit summary current
30 March 2024
- 18:3518:35, 30 March 2024 diff hist +214 m Tangent of Sum of Series of Angles/Proof 1 No edit summary current
- 02:3902:39, 30 March 2024 diff hist 0 m Tangent of Sum of Series of Angles No edit summary current
- 02:3802:38, 30 March 2024 diff hist +65 Category:Tangent of Sum of Series of Angles No edit summary current
- 02:3402:34, 30 March 2024 diff hist +29 N Category:Tangent of Sum of Series of Angles Created page with "Category:Tangent Function"
- 02:3302:33, 30 March 2024 diff hist +1,754 N Tangent of Sum of Series of Angles/Proof 2 Created page with "== Theorem == {{:Tangent of Sum of Series of Angles}} == Proof == <onlyinclude> First we note: {{begin-eqn}} {{eqn | l = \cos \sum_j \theta_j + i \sin \sum_j \theta_j | r = \prod_j \paren {\cos \theta_j + i \sin \theta_j} | c = Product of Complex Numbers in Polar Form }} {{eqn | r = \prod_j \cos \theta_j \prod_j \paren {1 + i \tan \theta_j} | c = }} {{eqn | r = \prod_j \cos \theta_j \paren {1 + i \tan \theta_1} \times \paren {1 + i \tan \theta_2}..."
- 02:3202:32, 30 March 2024 diff hist +3,782 N Tangent of Sum of Series of Angles/Proof 1 Created page with "== Theorem == {{:Tangent of Sum of Series of Angles}} == Proof == <onlyinclude> First we note: {{begin-eqn}} {{eqn | l = \cos \sum_j \theta_j + i \sin \sum_j \theta_j | r = \prod_j \paren {\cos \theta_j + i \sin \theta_j} | c = Product of Complex Numbers in Polar Form }} {{eqn | r = \prod_j \cos \theta_j \prod_j \paren {1 + i \tan \theta_j} | c = }} {{eqn | r = \prod_j \cos \theta_j \paren {1 + i \tan \theta_1} \times \paren {1 + i \tan \theta_2}..."
- 02:3202:32, 30 March 2024 diff hist −3,356 Tangent of Sum of Series of Angles No edit summary
29 March 2024
- 22:1722:17, 29 March 2024 diff hist +2,921 Tangent of Sum of Series of Angles This should be a tad clearer...
- 00:3700:37, 29 March 2024 diff hist +626 Tangent of Sum of Series of Angles Very unclear proof.
27 March 2024
- 22:1522:15, 27 March 2024 diff hist +431 Talk:Triple Angle Formulas/Tangent No edit summary
25 March 2024
- 01:4001:40, 25 March 2024 diff hist +8 m Integral Representation of Bernoulli Number No edit summary current
24 March 2024
- 16:0116:01, 24 March 2024 diff hist −89 m Integral Representation of Bernoulli Number No edit summary
- 16:0016:00, 24 March 2024 diff hist +2,304 N Integral Representation of Bernoulli Number Created page with "== Theorem == <onlyinclude> Bernoulli numbers can be expressed in integral form as follows: :$\ds \size {B_{2 n} } = 4 n \int_0^\infty \frac {t^{2 n - 1} } {e^t - 1} \rd t$ where: :$B_n$ are the Bernoulli numbers :$n$ is a positive integer. </onlyinclude> == Proof == {{begin-eqn}} {{eqn | l = \map \zeta s \map \Gamma s | r = \int_0^\infty \frac {t^{s - 1} } {e^t -..."
23 March 2024
- 19:0619:06, 23 March 2024 diff hist −21 m Binet's Formula for Logarithm of Gamma Function/Formulation 1 No edit summary current
- 18:5818:58, 23 March 2024 diff hist +429 Talk:Main Page No edit summary
20 March 2024
- 02:0702:07, 20 March 2024 diff hist +173 m Binet's Formula for Logarithm of Gamma Function/Formulation 1 No edit summary
- 02:0402:04, 20 March 2024 diff hist +6,039 Binet's Formula for Logarithm of Gamma Function/Formulation 2 No edit summary current
- 02:0302:03, 20 March 2024 diff hist +1,559 N Binet's Formula for Logarithm of Gamma Function/Formulation 1/Corollary Created page with "== Corollary to Binet's Formula for Logarithm of Gamma Function/Formulation 1 == <onlyinclude> Let $z$ be a complex number with a positive real part. Then: :$\ds \lim_{z \mathop \to \infty} \size {\Ln \map \Gamma z - \paren {z - \frac 1 2} \Ln z + z - \frac 1 2 \ln 2 \pi } \to 0$ where: :$\Gamma$ is the Gamma function :$\Ln$ is the Definiti..."
17 March 2024
- 16:0816:08, 17 March 2024 diff hist +93 m Riemann Zeta Function as a Multiple Integral Riemann Zeta Function as Integral of Product seems a more fitting name current
- 00:0700:07, 17 March 2024 diff hist +106 m Abel-Plana Formula No edit summary
16 March 2024
- 22:0322:03, 16 March 2024 diff hist +1,301 N Abel-Plana Formula 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..."
- 16:1816:18, 16 March 2024 diff hist +25 m Mathematician:Niels Henrik Abel No edit summary
- 15:5215:52, 16 March 2024 diff hist +213 m Properties of Digamma Function No edit summary current
- 15:5115:51, 16 March 2024 diff hist +27 m Dirichlet's Integral Form of Digamma Function No edit summary
- 15:5115:51, 16 March 2024 diff hist +27 m Gauss's Integral Form of Digamma Function No edit summary current