In the context of Stirling's formula for gamma functions and bounds for ratios of gamma functions, this work has a threefold purpose: (1) Outline recently published literature; (2) Synthesize techniques and results from Bhattacharjee and Mukhopadhyay (Commun Stat, Theory & Methods 39:1046–1053,...
Explanation:Returns the number of ways to choose some number of objects from a pool of a given size of objects. COMBINA Syntax:COMBINA(n, k) Explanation:Returns the number of ways to choose some number of objects from a pool of a given size of objects, including ways that choose the s...
The gamma function \(\Gamma ( x ) =\int_{0}^{\infty}t^{x-1}e^{-t}\,dt\) for \(x>0\) is a generalization of the factorial function n! and has important applications in various branches of mathematics; see, for example, [1, 2, 3, 4, 5, 6] and the references cited ...
Related to Stirling's formula: Gamma function, Wolfram AlphaStirling's formula n (Mathematics) a formula giving the approximate value of the factorial of a large number n, as n! (n/e)n√(2πn) [named after James Stirling (1692–1770), Scottish mathematician] Collins English Dictionary –...
The gamma function \\(\\Gamma ( x ) =\\int_{0}^{\\infty}t^{x-1}e^{-t}\\,dt\\) for \\(x>0\\) is a generalization of the factorial function n! and has important applications in various branches of mathematics; see, for example, [1, 2, 3, 4, 5, 6] and the ...
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Related to Stirling's Formula:Gamma function,Wolfram Alpha Stirling's formula [′stir·liŋz ‚fȯr·myə·lə] (mathematics) The expression (n/e)n√(2πn) is asymptotic to factorialn;that is, the limit asngoes to ∞ of their ratio is 1. ...
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for any f∈X, where Γ is the Gamma function. This identity coincides with the celebrated classical formula of Bourgain, Brezis, and Mironescu [12, 22] when X=Lp(Rn), but it is new for general X, in particular for X=Lq(Rn) (1≤p<q<∞). Translation invariance plays a vital role...