Mercator series information

In mathematics, the Mercator series or Newton–Mercator series is the Taylor series for the natural logarithm: ln ⁡ ( 1 + x ) = x − x 2 2 + x 3 3 − x 4...

The transverse Mercator map projection (TM, TMP) is an adaptation of the standard Mercator projection. The transverse version is widely used in national...

{x^{3}}{3}}-\cdots .\end{aligned}}} The last series is known as Mercator series, named after Nicholas Mercator (since it was published in his 1668 treatise...

Mercator is a series of combine harvesters produced by the German agricultural company Claas in Harsewinkel. Initially called Senator, the Mercator series...

Gerardus Mercator Rumold Mercator, a 16th-century cartographer Nicholas Mercator, a 17th-century mathematician Mercator series, a representation of the...

The Universal Transverse Mercator (UTM) is a map projection system for assigning coordinates to locations on the surface of the Earth. Like the traditional...

on logarithms, published in 1668. In this treatise he described the Mercator series: ln ⁡ ( 1 + x ) = x − 1 2 x 2 + 1 3 x 3 − 1 4 x 4 + ⋯ . {\displaystyle...

sums to 1/3. The alternating harmonic series has a finite sum but the harmonic series does not. The Mercator series provides an analytic expression of the...

\end{aligned}}} This is the Taylor series for ln ⁡ x {\displaystyle \ln x} around 1. A change of variables yields the Mercator series: ln ⁡ ( 1 + x ) = ∑ k = 1...

Rumold Mercator (Leuven, 1541 – Duisburg, 31 December 1599) was a cartographer and the son of cartographer Gerardus Mercator. He completed some at the...

modern concept used in computing. Matrix logarithm Mel scale Mercator projection Mercator series Moment magnitude scale John Napier Napierian logarithm Natural...

important arbitrary dimension n identity can be obtained from the Mercator series expansion of the logarithm when the expansion converges. If every eigenvalue...

whose logarithm one attempts to take is invertible.) Then, by the Mercator series log ⁡ ( 1 + x ) = x − x 2 2 + x 3 3 − x 4 4 + ⋯ {\displaystyle \log(1+x)=x-{\frac...

negative real numbers from the complex plane. Another example: The Mercator series ln ⁡ ( 1 + u ) = ∑ n = 1 ∞ ( − 1 ) n + 1 n u n = u − u 2 2 + u 3 3...

convergence, an alternating series called the Mercator series expresses the logarithm function over the interval (0,2). Since the series is negative in (0,1)...

hindawi.com/archive/2013/412958.pdf [bare URL PDF] Weisstein, Eric W. "Mercator Series". MathWorld--A Wolfram Web Resource. Retrieved 2024-04-24. Flajolet...

their own work on infinitesimal calculus. History of group theory Mercator series Tangent Wikimedia Commons has media related to Johannes Hudde. J.P...

=e^{D}-1} where D is differentiation with respect to x, we have, from the Mercator series, D e D − 1 = log ⁡ ( Δ + 1 ) Δ = ∑ n = 0 ∞ ( − Δ ) n n + 1 . {\displaystyle...

The Martin P4M Mercator was a maritime reconnaissance aircraft built by the Glenn L. Martin Company. The Mercator was an unsuccessful contender for a United...

onto a plane.[citation needed] The most well-known map projection is the Mercator projection.: 45  This map projection has the property of being conformal...

{ad} _{Z}\|<\log 2~~,\end{aligned}}} the last step by virtue of the Mercator series expansion, it follows that and, thus, integrating, Z ( 1 ) = ∫ 0 1...

Saint-Vincent - Jesuit mathematician who independently discovered the Mercator series, the expansion of log (1 + x) in ascending powers of x Saint Francis...

reputation of the work of Gerard Mercator, and for his portraits of Francis Drake. He inherited and republished the plates of Mercator, thus reviving his legacy...