mathematics, the arctangent series, traditionally called Gregory's series, is the Taylor series expansion at the origin of the arctangent function: arctan...

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...

the power series expansions of sine, cosine, tangent, and arctangent. Using the Taylor series approximations of sine and cosine, he produced a sine table...

Commonly Called Algebra. Gottfried Wilhelm Leibniz rediscovers the arctangent series and obtains the Leibniz formula for π as the special case. Samuel...

{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...

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...

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...

suggest that he found the Taylor series for the trigonometric functions of sine, cosine, and arctangent (see Madhava series). During the following two centuries...

− 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...

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...

the power series expansion of the arctangent function using some knowledge of differentiation, integration and the sum of a geometric series. The derivative...

as Madhava series. The series for arctangent is sometimes called Gregory's series or the Gregory–Leibniz series. Madhava used infinite series to estimate...

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...

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...

\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 −...

then the second equation is indeterminate. If the standard 2-argument arctangent atan2 function is used, then these values are usually handled correctly...

{\displaystyle \operatorname {tg} } is used in several European languages). Arctangent may be denoted arctan {\displaystyle \arctan } , atan {\displaystyle \operatorname...

infinite series expansions, now called Taylor series, of functions such as sine, cosine, tangent and arctangent. Alongside his development of Taylor series of...

many contributions, he discovered infinite series for the trigonometric functions of sine, cosine, arctangent, and many methods for calculating the circumference...

y}{\cosh x}}.} (In practical implementation, make sure to use the 2-argument arctangent, u = atan2 ⁡ ( sinh ⁡ x , cos ⁡ y ) {\textstyle u=\operatorname {atan2}...

described by the Pythagorean theorem. An analogous unit circle results in the arctangent of the circle trigonometric with the described area allocation. The following...

}{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...

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...

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...

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, [...

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...

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:...

Trigonometric substitution Integrals (inverse functions) Derivatives Trigonometric series Mathematicians Hipparchus Ptolemy Brahmagupta al-Hasib al-Battani Regiomontanus...

conjunction with Gregory's series, the Taylor series expansion for arctangent: The angle addition formula for arctangent asserts that if − π 2 < arctan...

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 −...