Who can give me some function with asymptotics ?

In summary, asymptotics in mathematics refers to the behavior of a function as the input approaches a certain value, typically infinity. It is important in studying functions to understand their long-term behavior and make predictions about their growth or decay. An example of a function with asymptotics is the logarithmic function, which has an asymptote at the y-axis. Mathematicians and scientists often use asymptotics in their research and can provide functions with known asymptotics. Asymptotics can be applied in various mathematical and scientific fields to analyze and make predictions about the behavior of functions and solve complex problems.
  • #1
sufive
23
0
Dear Everybody,

I need some some function f(r) with asymptotics

as x -> 0, f-> 1*x+a*x^3+b*x^5+c*x^7+..., a,b,c>0
as x -> infinity, f-> x*Log[x]

I construct one like A/B*Log[1+x], where A=1+x/2+x^3/12, B=1+d*x^2.
But I think it is too complex, such that I cannot continue my successive latter works.

Can somebody give me a more simple such functions?

Suggestion or hints are also welcome.

Thank you very much!
 
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  • #2
1/x works. Asymptotes are the y and x axes.
 

FAQ: Who can give me some function with asymptotics ?

What is the definition of asymptotics in mathematics?

Asymptotics in mathematics refers to the behavior of a function as the input approaches a certain value, typically infinity. It describes how a function grows or decays as its input increases or decreases without bound.

Why is it important to consider asymptotics when studying functions?

Asymptotics allows us to understand the long-term behavior of a function and make predictions about its growth or decay. It is particularly useful in areas such as calculus, number theory, and probability theory.

Can you give an example of a function with asymptotics?

One example is the logarithmic function, which has an asymptote at the y-axis. As the input approaches infinity, the function approaches the x-axis, but never crosses it. This behavior is described by the asymptote of the function.

Who can provide me with a function with known asymptotics?

Mathematicians and scientists often use asymptotics in their research and can provide functions with known asymptotics. There are also many online resources and textbooks that contain examples of functions with asymptotics.

How can I use asymptotics in my own research or studies?

Asymptotics can be used to analyze and make predictions about the behavior of functions, as well as to solve problems in various mathematical and scientific fields. It is a powerful tool for understanding the behavior of complex functions and systems.

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