In real analysis, a branch of mathematics, a slowly varying function is a function of a real variable whose behaviour at infinity is in some sense similar to the behaviour of a function converging at infinity. Similarly, a regularly varying function is a function of a real variable whose behaviour at infinity is similar to the behaviour of a power law function (like a polynomial) near infinity. These classes of functions were both introduced by Jovan Karamata,[1][2] and have found several important applications, for example in probability theory.
^See (Galambos & Seneta 1973)
^See (Bingham, Goldie & Teugels 1987).
and 24 Related for: Slowly varying function information
a slowly varying function. For any β ∈ R, the function L(x) = log β x is slowlyvarying. The function L(x) = x is not slowlyvarying, nor is L(x) = x β...
Arrhenius exponential (of enthalpy rather than energy) multiplied by a slowlyvaryingfunction of T. The precise form of the temperature dependence depends upon...
approximation is valid is that the z derivative of the amplitude function u is a slowlyvaryingfunction of z: | ∂ 2 u ∂ z 2 | ≪ | k ∂ u ∂ z | . {\displaystyle...
proportional to nc, for any c ≥ 1/2; it may also be multiplied by a slowlyvaryingfunction of n. The law of the iterated logarithm specifies what is happening...
\alpha >1} , and L ( x ) {\displaystyle L(x)} is a slowlyvaryingfunction, which is any function that satisfies lim x → ∞ L ( r x ) / L ( x ) = 1 {\displaystyle...
longitude) is considered to be a slowlyvaryingfunction, modeled with a Maclaurin series, rather than a simple linear function of time. Mean longitude, like...
where σ > 0 {\displaystyle \sigma >0} and L {\displaystyle L} is a slowlyvaryingfunction, then [ z n ] f ( z ) ∼ n σ − 1 Γ ( σ ) L ( n ) {\displaystyle...
analysis, in particular, the Tauberian theory and the theory of slowlyvaryingfunctions. Considered to be among the most influential Serbian mathematicians...
A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support...
popularity, the function initial rate of tumor growth is difficult to predetermine given the varying microcosms present with a patient, or varying environmental...
(as in radar applications) a(t) is a slowlyvaryingfunction of time and the phase θ(t) is oscillatory and varies rapidly, over the range of integration...
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation f ( x ) = L 1 + e − k ( x − x 0 ) {\displaystyle f(x)={\frac...
{\displaystyle r(k)\sim k^{-d}L(k)} as k→∞ and where L(k) is a slowlyvaryingfunction at large values of k, this sequence is called a self-similar process...
the gamma function (often given the name lgamma or lngamma in programming environments or gammaln in spreadsheets); this grows much more slowly, and for...
The exponential function is a mathematical function denoted by f ( x ) = exp ( x ) {\displaystyle f(x)=\exp(x)} or e x {\displaystyle e^{x}} (where...
_{a}^{b}f(x)g(x)dx} where f ( x ) {\textstyle f(x)} is a relatively slowly-varyingfunction and g ( x ) {\textstyle g(x)} is either sine or cosine or a complex...
In electrical engineering, a function generator is usually a piece of electronic test equipment or software used to generate different types of electrical...
faster than exponential functions, but much more slowly than double exponential functions. However, tetration and the Ackermann function grow faster. See Big...
necessarily constant, and are functions of time albeit slowlyvaryingfunctions of time. Stated differently these functions of time are bandlimited to much...
recast as an exponential function, semiclassically expanded, and then either the amplitude or the phase is taken to be changing slowly. The name is an initialism...
transformation is good in time resolution of high frequencies, while for slowlyvaryingfunctions, the frequency resolution is remarkable. Another example: The analysis...
contain(s) all three types, although in varying proportions. Traditionally, fibers were categorized depending on their varying color, which is a reflection of...
Global Information