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A general 1-form is a linear combination of these differentials at every point on the manifold: + +, where the f k = f k (x 1, ... , x n) are functions of all the coordinates. A differential 1-form is integrated along an oriented curve as a line integral.
In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of the cotangent bundle. [1] Equivalently, a one-form on a manifold is a smooth mapping of the total space of the tangent bundle of to whose restriction to each fibre is a linear functional on the ...
In mathematics, a linear form (also known as a linear functional, [1] a one-form, or a covector) is a linear map [nb 1] from a vector space to its field of scalars (often, the real numbers or the complex numbers).
2.1 Low-order polylogarithms. ... The following is a useful property to calculate low-integer-order polylogarithms recursively in closed form: ... (mathematics) List ...
The apparent plural form in English goes back to the Latin neuter plural mathematica , based on the Greek plural ta mathēmatiká (τὰ μαθηματικά) and means roughly "all things mathematical", although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of ...
As a complex number, i can be represented in rectangular form as 0 + 1i, with a zero real component and a unit imaginary component. In polar form , i can be represented as 1 × e πi /2 (or just e πi /2 ), with an absolute value (or magnitude) of 1 and an argument (or angle) of π 2 {\displaystyle {\tfrac {\pi }{2}}} radians .
1 Mathematics and human activities. ... Mathematics, Form and Function, a book published in 1986 by Springer-Verlag, is a survey of the whole of mathematics, ...
1 (one, unit, unity) is a number, numeral, and glyph.It is the first and smallest positive integer of the infinite sequence of natural numbers.This fundamental property has led to its unique uses in other fields, ranging from science to sports, where it commonly denotes the first, leading, or top thing in a group. 1 is the unit of counting or measurement, a determiner for singular nouns, and a ...