A good example of such kind of problem is whether the anti-derivative of a given function can be expressed through elementary functions.
Have a look at
Maxwell Rosenlicht. Integration in Finite Terms. The American Mathematical Monthly
Vol. 79, No. 9 (Nov., 1972), pp. 963-972
http://www.jstor.org/stable/2318066?seq=1#page_scan_tab_contents
A good example of such kind of problem is whether the anti-derivative of a given function can be expressed through elementary functions.
Have a look at
Maxwell Rosenlicht. Integration in Finite Terms. The American Mathematical Monthly
Vol. 79, No. 9 (Nov., 1972), pp. 963-972
http://www.jstor.org/stable/2318066?seq=1#page_scan_tab_contents
Dear Sawon,
George has right, the words "analytic solution" in your question can be understood in two different ways: 1) an explicit expression through standard functions, and 2) analytic in the sense that every point in the domain has a neighborhood, in which the solution can be expanded in Taylor series. So, what did you mean in your question?
Best, Vladimir
My understanding analytic work as following [1] Below and ruler and compass as [2] below:
[1] http://www.stefanides.gr/Html/Classical_Problems_et_Alii_with_Web_Links.html#Tracing_ARCHIMEDES_Method_Of_Polygons_for_“CIRCLE_MEASUREMENT”_
[2]
http://www.stefanides.gr/Html/piquad.html
Regards
To build a space in which the given problem can be reduced to some other problem known as not having any analytical solution.
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