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Does this function belong to an interesting class of functions? 
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#1
Dec211, 06:55 AM

P: 610

Hello and thanks for your consideration,
I'd like some insight into the function [itex]f(\phi) = \frac {1  \phi}{\phi  1}[/itex] Does this apply to any known modeling situations? Is it recognized as belonging to a more general class of functions that may have interesting or unique characteristics? Or can the function be transformed into a function that does? 


#2
Dec211, 07:45 AM

HW Helper
P: 1,391

Your function, as written, is just equal to 1, except when [itex]\phi = 1[/itex], where there is a discontinuity because the denominator vanishes there.
If you want an example of a function that has a similar form but isn't trivially some constant and has some applications, see Mobius transformation. (But note that the Mobius transformation is usually used with complex numbers. I don't know if it is used much in real number applications). 


#3
Dec211, 08:52 AM

P: 610

Thanks, an association with the Mobius transformation does yield many interesting things to think about, especially since [itex]\phi[/itex] can be complex in the situation where the function popped up.
We could argue that the value becomes 1 when [itex]\phi = 1[/itex] couldn't we? This almost sounds like a spinning sphere where the axis must be aligned parallel to a force acting on the sphere, but which can suddenly undergo a spin flip. 


#4
Dec211, 10:06 AM

Sci Advisor
P: 3,286

Does this function belong to an interesting class of functions?



#5
Dec211, 02:04 PM

Math
Emeritus
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Thanks
PF Gold
P: 39,503




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