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Taylor's theorem is named after the mathematician Brook Taylor, who stated a version of it in 1715, [2] although an earlier version of the result was already mentioned in 1671 by James Gregory. [3] Taylor's theorem is taught in introductory-level calculus courses and is one of the central elementary tools in mathematical analysis.
It is possible to include both Dirac and Majorana mass terms in the same theory, which (in contrast to the Dirac-mass-only approach) can provide a “natural” explanation for the smallness of the observed neutrino masses, by linking the right-handed neutrinos to yet-unknown physics around the GUT scale [6] (see seesaw mechanism).
More generally, if g is C k, α (with k larger than one) and Ric(g) is C l, α relative to some coordinate charts, then the transition function to a harmonic coordinate chart will be C k + 1, α, and so Ric(g) will be C min(l, k), α in harmonic coordinate charts. So, by the previous result, g will be C min(l, k) + 2, α in harmonic coordinate ...
Michael Danos and Johann Rafelski edited the Pocketbook of Mathematical Functions, published by Verlag Harri Deutsch in 1984. [14] [15] The book is an abridged version of Abramowitz's and Stegun's Handbook, retaining most of the formulas (except for the first and the two last original chapters, which were dropped), but reducing the numerical tables to a minimum, [14] which, by this time, could ...
1.6.2 Using the Taylor series and Newton's method ... 3.2.1.2 Operations on two independent ... distribution can be re-scaled and shifted via the formula = ...
In 1706, John Machin used Gregory's series (the Taylor series for arctangent) and the identity = to calculate 100 digits of π (see § Machin-like formula below). [ 30 ] [ 31 ] In 1719, Thomas de Lagny used a similar identity to calculate 127 digits (of which 112 were correct).
Viscosity is a measure of a fluid's rate-dependent resistance to a change in shape or to movement of its neighboring portions relative to one another. [1] For liquids, it corresponds to the informal concept of thickness; for example, syrup has a higher viscosity than water. [2]
A Kähler manifold is a Riemannian manifold of even dimension whose holonomy group is contained in the unitary group (). [3] Equivalently, there is a complex structure on the tangent space of at each point (that is, a real linear map from to itself with =) such that preserves the metric (meaning that (,) = (,)) and is preserved by parallel transport.