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There is a page named "Leibniz formula for pi" on Wikipedia
- In mathematics, the Leibniz formula for π, named after Gottfried Wilhelm Leibniz, states that π 4 = 1 − 1 3 + 1 5 − 1 7 + 1 9 − ⋯ = ∑ k = 0 ∞ ( − 1 ) k...9 KB (1,509 words) - 07:34, 10 July 2024
- subfield of number theory devoted to generalising formulae such as the Leibniz formula for pi, namely 1 − 1 3 + 1 5 − 1 7 + 1 9 − ⋯ = π 4 , {\displaystyle 1\...5 KB (573 words) - 14:55, 23 June 2024
- called the Gregory–Leibniz series, equals π 4 {\textstyle {\frac {\pi }{4}}} when evaluated with z = 1 {\displaystyle z=1} . But for z = 1 {\displaystyle...146 KB (17,390 words) - 14:59, 17 August 2024
- List of topics related to π (redirect from List of pi topics)identity Six nines in pi Gauss–Legendre algorithm Gaussian function History of π A History of Pi (book) Indiana Pi Bill Leibniz formula for pi Lindemann–Weierstrass...3 KB (159 words) - 00:58, 18 January 2024
- List of formulae involving π (redirect from List of formula for pi){1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}-\cdots =\arctan {1}={\frac {\pi }{4}}} (see Leibniz formula for pi) ∑ n = 0 ∞ ( − 1 ) ( n 2 − n ) / 2 2 n + 1 = 1 + 1 3 − 1...37 KB (7,842 words) - 18:06, 23 August 2024
- for arctangent, we have G x = arctan 1 x . {\displaystyle G_{x}=\arctan {\frac {1}{x}}.} Setting x = 1 gives the well-known Leibniz formula for pi....1 KB (150 words) - 22:57, 29 December 2023
- calculus, the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of...52 KB (11,174 words) - 01:19, 19 August 2024
- replaced by using the formula to calculate the diagonal term. For a simple-but-concrete example, recall the Leibniz formula for pi The algorithm described...4 KB (315 words) - 18:52, 28 November 2023
- Approximations of π (redirect from Formula for pi)Approximations for the mathematical constant pi (π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning...87 KB (12,455 words) - 11:31, 15 August 2024
- Chronology of computation of π (redirect from Chronology of computations of pi)numerical values of, or bounds on, the mathematical constant pi (π). For more detailed explanations for some of these calculations, see Approximations of π. As...41 KB (1,619 words) - 07:25, 18 August 2024
- William Brouncker, 2nd Viscount Brouncker (redirect from Brouncker's formula){9^{2}}{2+\ddots }}}}}}}}}}}}} The convergents are related to the Leibniz formula for pi: for instance 1 1 + 1 2 2 = 2 3 = 1 − 1 3 {\displaystyle {\frac {1}{1+{\frac...9 KB (969 words) - 19:20, 24 November 2023
- }{2\pi i}}\oint _{\gamma }{\frac {f(z)}{\left(z-a\right)^{n+1}}}\,dz.} This formula is sometimes referred to as Cauchy's differentiation formula. The...25 KB (4,364 words) - 15:38, 13 August 2024
- Gottfried Wilhelm Leibniz (1 July 1646 [O.S. 21 June] – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and...152 KB (18,823 words) - 07:00, 20 August 2024
- {P}}_{n,k}=\{(\pi _{1},\pi _{2},\dots ,\pi _{n})\,:\ \pi _{1}+\pi _{2}+\cdots +\pi _{n}=k,\ \pi _{1}\cdot 1+\pi _{2}\cdot 2+\cdots +\pi _{n}\cdot n=n\}}...20 KB (3,741 words) - 18:56, 13 August 2024
- In abstract algebraic logic, a branch of mathematical logic, the Leibniz operator is a tool used to classify deductive systems, which have a precise technical...7 KB (1,167 words) - 22:44, 6 April 2023
- John Machin (redirect from Machin's formula){\displaystyle {\frac {\pi }{4}}=4\arctan {\frac {1}{5}}-\arctan {\frac {1}{239}}} The benefit of the new formula, a variation on the Gregory–Leibniz series (π/4 = arctan 1)...5 KB (442 words) - 01:47, 14 May 2024
- Differentiation rules (redirect from Differentiation formulas)This formula is the general form of the Leibniz integral rule and can be derived using the fundamental theorem of calculus. Some rules exist for computing...16 KB (2,763 words) - 10:37, 26 June 2024
- the Leibniz formula for π, or recently sometimes the Mādhava–Leibniz formula: π 4 = arctan 1 = 1 − 1 3 + 1 5 − 1 7 + ⋯ . {\displaystyle {\frac {\pi }{4}}=\arctan...17 KB (2,374 words) - 07:22, 19 May 2024
- Integration by substitution (redirect from Change of variables formula)substitution as a partial justification of Leibniz's notation for integrals and derivatives. The formula is used to transform one integral into another...19 KB (3,310 words) - 11:56, 4 June 2024
- Gottfried Leibniz in 1673, and is conventionally called Gregory's series. The specific value arctan 1 = 1 4 π {\textstyle \arctan 1={\tfrac {1}{4}}\pi } can...33 KB (4,624 words) - 15:08, 23 June 2024
- to: Pi Day Exploratorium's Pi Day Web Site 10 pi facts for the most irrational Pi Day of your life (2015) NPR provides a "Pi Rap" audiovideo Pi Day Professor
- his lectures were so obscure that none except Leibniz could understand them. Later on, Leibniz attended, for a half-year, at Jena, the lectures of Erhard
- {\displaystyle n} tends to infinity. Leibniz' formula for π {\displaystyle \pi } is a special case of the Gregory's series for the arctangent, arctan x = x