mathematics, the arctangent series, traditionally called Gregory's series, is the Taylor series expansion at the origin of the arctangent function: arctan...
17 KB (2,374 words) - 07:22, 19 May 2024
In mathematics, a Madhava series is one of the three Taylor series expansions for the sine, cosine, and arctangent functions discovered in 14th or 15th...
33 KB (4,624 words) - 15:08, 23 June 2024
the power series expansions of sine, cosine, tangent, and arctangent. Using the Taylor series approximations of sine and cosine, he produced a sine table...
50 KB (6,365 words) - 17:27, 12 August 2024
Commonly Called Algebra. Gottfried Wilhelm Leibniz rediscovers the arctangent series and obtains the Leibniz formula for π as the special case. Samuel...
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Inverse trigonometric functions (redirect from Arctangent)
{1-z^{2}}}}} , as a binomial series, and integrating term by term (using the integral definition as above). The series for arctangent can similarly be derived...
76 KB (10,711 words) - 06:59, 5 August 2024
Leapster (redirect from Leapster series)
WALL-E Wolverine and the X-Men Word Chasers CPU: Custom ASIC containing an ARCTangent-A5 CPU, running at 96 MHz. Memory: Original Leapster: 2 MB onboard RAM...
13 KB (1,196 words) - 19:32, 17 August 2024
Polylogarithm (redirect from Arctangent integral)
Li3(z) The polylogarithm function is defined by a power series in z, which is also a Dirichlet series in s: Li s ( z ) = ∑ k = 1 ∞ z k k s = z + z 2 2 s...
60 KB (10,165 words) - 14:52, 17 June 2024
suggest that he found the Taylor series for the trigonometric functions of sine, cosine, and arctangent (see Madhava series). During the following two centuries...
48 KB (8,253 words) - 02:02, 23 August 2024
− x {\displaystyle f(x)=\tanh x={\frac {e^{x}-e^{-x}}{e^{x}+e^{-x}}}} Arctangent function f ( x ) = arctan x {\displaystyle f(x)=\arctan x} Gudermannian...
13 KB (1,688 words) - 07:27, 10 May 2024
Approximations of π (section Arctangent)
found the Maclaurin series for arctangent, and then two infinite series for π. One of them is now known as the Madhava–Leibniz series, based on π = 4 arctan...
87 KB (12,455 words) - 11:31, 15 August 2024
the power series expansion of the arctangent function using some knowledge of differentiation, integration and the sum of a geometric series. The derivative...
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Pi (category Mathematical series)
as Madhava series. The series for arctangent is sometimes called Gregory's series or the Gregory–Leibniz series. Madhava used infinite series to estimate...
146 KB (17,390 words) - 14:59, 17 August 2024
positive z-axis and so needs to perform a rotation of value equal to the arctangent of 1⁄√2 which is approximately 35.264°. There are eight different orientations...
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infinite series involving π are: where ( x ) n {\displaystyle (x)_{n}} is the Pochhammer symbol for the rising factorial. See also Ramanujan–Sato series. π...
37 KB (7,842 words) - 18:06, 23 August 2024
\operatorname {arccsc} {\frac {1}{x}}=\arcsin x} The arctangent function can be expanded as a series: arctan ( n x ) = ∑ m = 1 n arctan x 1 + ( m −...
81 KB (12,166 words) - 04:35, 2 August 2024
then the second equation is indeterminate. If the standard 2-argument arctangent atan2 function is used, then these values are usually handled correctly...
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{\displaystyle \operatorname {tg} } is used in several European languages). Arctangent may be denoted arctan {\displaystyle \arctan } , atan {\displaystyle \operatorname...
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infinite series expansions, now called Taylor series, of functions such as sine, cosine, tangent and arctangent. Alongside his development of Taylor series of...
45 KB (4,351 words) - 16:08, 7 August 2024
Madhava of Sangamagrama (category Mathematical series)
many contributions, he discovered infinite series for the trigonometric functions of sine, cosine, arctangent, and many methods for calculating the circumference...
33 KB (3,711 words) - 12:46, 23 July 2024
Gudermannian function (section Taylor series)
y}{\cosh x}}.} (In practical implementation, make sure to use the 2-argument arctangent, u = atan2 ( sinh x , cos y ) {\textstyle u=\operatorname {atan2}...
38 KB (5,369 words) - 03:02, 5 August 2024
Lemniscate elliptic functions (section First proof: comparison with the derivative of the arctangent)
described by the Pythagorean theorem. An analogous unit circle results in the arctangent of the circle trigonometric with the described area allocation. The following...
124 KB (22,474 words) - 17:12, 25 August 2024
Inverse hyperbolic functions (redirect from Hyperbolic arctangent)
}{dx}}={\frac {1}{dx/d\theta }}={\frac {1}{\sqrt {1+x^{2}}}}.} Expansion series can be obtained for the above functions: arsinh x = x − ( 1 2 ) x 3 3...
27 KB (4,208 words) - 20:38, 15 July 2024
radix R {\displaystyle R} showed that for the functions sine, cosine, arctangent, it is enough to perform R − 1 {\displaystyle R-1} iterations for each...
71 KB (7,227 words) - 05:13, 19 August 2024
for the nth root and logarithm functions, 0 is a branch point; for the arctangent function, the imaginary units i and −i are branch points. Using the branch...
9 KB (1,299 words) - 17:02, 17 July 2024
together to place the angle in the correct quadrant, using a two-argument arctangent function. Now consider the first column of a 3 × 3 rotation matrix, [...
99 KB (15,019 words) - 17:05, 31 July 2024
one-argument arctangent of the ratio s t ( 1 ) s t ( 0 ) {\displaystyle {\frac {st(1)}{st(0)}}} : If both st(0) and st(1) are ±∞, then the arctangent is computed...
212 KB (12,382 words) - 21:53, 19 August 2024
a modern explanation of Jyeṣṭhadeva's proof of the power series expansion of the arctangent function: Victor J. Katz (2009). "12". A history of mathematics:...
11 KB (1,007 words) - 17:34, 13 February 2024
List of integrals of inverse trigonometric functions (section Arctangent function integration formulas)
Trigonometric substitution Integrals (inverse functions) Derivatives Trigonometric series Mathematicians Hipparchus Ptolemy Brahmagupta al-Hasib al-Battani Regiomontanus...
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conjunction with Gregory's series, the Taylor series expansion for arctangent: The angle addition formula for arctangent asserts that if − π 2 < arctan...
27 KB (4,643 words) - 20:31, 9 April 2024
can be solved for φ {\displaystyle \varphi } . Equating these gives the arctangent in terms of the natural logarithm arctan t = − i 2 ln 1 + i t 1 −...
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