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the Pi function, i.e. the Gamma function when offset to coincide with the factorial; the complete elliptic integral of the third kind; the fundamental groupoid; osmotic pressure; represents: Archimedes' constant (more commonly just called Pi), the ratio of a circle's circumference to its diameter; the prime-counting function
Given M(a, b, z), the four functions M(a ± 1, b, z), M(a, b ± 1, z) are called contiguous to M(a, b, z). The function M(a, b, z) can be written as a linear combination of any two of its contiguous functions, with rational coefficients in terms of a, b, and z. This gives (4 2) = 6 relations, given by identifying any two lines on the right hand ...
In two dimensions, the Levi-Civita symbol is defined by: = {+ (,) = (,) (,) = (,) = The values can be arranged into a 2 × 2 antisymmetric matrix: = () Use of the two-dimensional symbol is common in condensed matter, and in certain specialized high-energy topics like supersymmetry [ 1 ] and twistor theory , [ 2 ] where it appears in the context ...
Sigma's original name may have been san, but due to the complicated early history of the Greek epichoric alphabets, san came to be identified as a separate letter in the Greek alphabet, represented as Ϻ. [2] Herodotus reports that "san" was the name given by the Dorians to the same letter called "sigma" by the Ionians. [i] [3]
The sequence of Lucas numbers (not to be confused with the generalized Lucas sequences, of which this is part) is like the Fibonacci sequence, in that each term is the sum of the previous two terms and , however instead starts with , as the 0th and 1st terms and :
where k e is the Coulomb constant (k e ≈ 9 × 10 9 N⋅m 2 ⋅C −2), q 1 and q 2 are the signed magnitudes of the charges, and the scalar r is the distance between the charges. The force of the interaction between the charges is attractive if the charges have opposite signs (i.e., F is negative) and repulsive if like-signed (i.e., F is ...
The reason why this distribution is called "stable count" can be understood by the relation = /. Note that N {\displaystyle N} is the "count" of the Lévy sum. Given a fixed α {\displaystyle \alpha } , this distribution gives the probability of taking N {\displaystyle N} steps to travel one unit of distance.