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The Lorentz factor or Lorentz term (also known as the gamma factor [1]) is a dimensionless quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves.
By choosing an appropriate g (typically a small integer), only some 5–10 terms of the series are needed to compute the gamma function with typical single or double floating-point precision. If a fixed g is chosen, the coefficients can be calculated in advance and, thanks to partial fraction decomposition , the sum is recast into the following ...
The following notations are used very often in special relativity: Lorentz factor = where = and v is the relative velocity between two inertial frames.. For two frames at rest, γ = 1, and increases with relative velocity between the two inertial frames.
At any time after t = t′ = 0, xx′ is not zero, so dividing both sides of the equation by xx′ results in =, which is called the "Lorentz factor". When the transformation equations are required to satisfy the light signal equations in the form x = ct and x ′ = ct ′, by substituting the x and x'-values, the same technique produces the ...
Its SI unit is the radian per second per tesla (rad⋅s −1 ⋅T −1) or, equivalently, the coulomb per kilogram (C⋅kg −1). [citation needed] The term "gyromagnetic ratio" is often used [2] as a synonym for a different but closely related quantity, the g-factor. The g-factor only differs from the gyromagnetic ratio in being dimensionless.
The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic except at zero and the negative integers, where it has simple poles. The gamma function has no zeros, so the reciprocal gamma function 1 / Γ(z) is an entire function.
Prabhakar function is a certain special function in mathematics introduced by the Indian mathematician Tilak Raj Prabhakar in a paper published in 1971. [1] The function is a three-parameter generalization of the well known two-parameter Mittag-Leffler function in mathematics.
The Euler integral of the second kind is the gamma function [2] = For positive integers m and n , the two integrals can be expressed in terms of factorials and binomial coefficients : B ( n , m ) = ( n − 1 ) !