a slowly varying function. For any β ∈ R, the function L(x) = log β x is slowly varying. The function L(x) = x is not slowly varying, nor is L(x) = x β...
5 KB (587 words) - 00:43, 22 July 2024
Arrhenius exponential (of enthalpy rather than energy) multiplied by a slowly varying function of T. The precise form of the temperature dependence depends upon...
21 KB (2,788 words) - 21:20, 24 April 2024
Central limit theorem (section Density functions)
proportional to nc, for any c ≥ 1/2; it may also be multiplied by a slowly varying function of n. The law of the iterated logarithm specifies what is happening...
65 KB (8,861 words) - 09:16, 20 August 2024
Helmholtz equation (section Three-dimensional solutions given the function on a 2-dimensional plane)
approximation is valid is that the z derivative of the amplitude function u is a slowly varying function of z: | ∂ 2 u ∂ z 2 | ≪ | k ∂ u ∂ z | . {\displaystyle...
19 KB (2,965 words) - 21:20, 20 August 2024
( x ) = L ( x ) ⋅ x − 1 / ξ , for some ξ > 0 , where L is a slowly varying function. {\displaystyle {\bar {F}}(x)=1-F(x)=L(x)\cdot x^{-1/\xi },\,\...
20 KB (2,757 words) - 16:49, 4 September 2024
Power law (section Power-law functions)
\alpha >1} , and L ( x ) {\displaystyle L(x)} is a slowly varying function, which is any function that satisfies lim x → ∞ L ( r x ) / L ( x ) = 1 {\displaystyle...
61 KB (7,915 words) - 11:45, 13 September 2024
Stirling's approximation (category Gamma and related functions)
{\displaystyle n!} , one considers its natural logarithm, as this is a slowly varying function: ln ( n ! ) = ln 1 + ln 2 + ⋯ + ln n . {\displaystyle \ln(n...
27 KB (4,940 words) - 03:24, 30 August 2024
longitude) is considered to be a slowly varying function, modeled with a Maclaurin series, rather than a simple linear function of time. Mean longitude, like...
5 KB (576 words) - 09:55, 26 March 2024
components are no longer completely orthogonal functions. But when A(t) and φ(t) are slowly varying functions compared to 2πft, the assumption of orthogonality...
13 KB (1,505 words) - 00:25, 17 June 2024
Analytic combinatorics (section Meromorphic functions)
where σ > 0 {\displaystyle \sigma >0} and L {\displaystyle L} is a slowly varying function, then [ z n ] f ( z ) ∼ n σ − 1 Γ ( σ ) L ( n ) {\displaystyle...
8 KB (1,126 words) - 23:29, 12 September 2024