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Fri 25 May, 2012 04:01 am
Consider the functional equation f ( y ) + f ( 1 / y ) = 0 , it is easy to see that f ( y ) = h ( log y ) , where the logarithm can be taken with any base and " h " is an odd function , is a solution of the equation . Find any other solution ( if exists ) .
Well , I have been able to extend the solution ,
f ( y ) = h ( log y ) for y >0
f ( y ) = g ( log( - y ) ) for y <0
f ( y ) = F ( log y ) for all complex number y with Im(y) not zero.
( h , g , F are odd functions )
any other solution will be highly appreciated.
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