@Mac Dude when i eliminated the "is" i was simply inferring it from viewing by calling showstat(is) which outputs:

is := proc()
   1   if _EnvInside_assume = true then
   2     FAIL
       else
   3     `is/internal`(args)
       end if
end proc

@tomleslie 

No you have misunderstood. I never said  asympt "fails" i said the complete opposite, it succeeds in catching the error which is encountered when one uses this line to determine the asymptote:

and hence i was trying to determine the line of code in asympt that was responsible for successfully handling the error the above line could not, (in my original post, i referred and labelled this as "line B") so no, we are not referring to a function which does not have an asymptote.

But look, there is no need to be blatently insulting, nobody is forcing you to provide me with assistance and i will eventually work it out on my own so there really is no urgency nor any need for you to get yourself so excited. you have confirmed now that you did not properly understand my question so look dont worry about it

@tomleslie 

So, my question is, which line in showstat(asympt) is responsible for catching the error which line B as above encounters?

@Markiyan Hirnyk  well you asked how maple is related to the content of the post, i replied with the fact that the result was arrived at by observing evaluations performed by the maple CAS, and then you asked what Af stands for and i refered to its definition as the asymptotic series expansion of a function F with respect to z, to the first N terms. which was explained above. so thats about as serious answer as you can get for the questions you have asked me.

@Markiyan Hirnyk  1. the maple CAS is what computed the result 2. what i say it is in the first sentence at the top of the page.

@Carl Love  and also, the help page also mentions that if we set a=infinity, the asymptotic series for the function will be returned. but  the output of showstat(asymt) shows me that several lines call the series() function itself. Apart from that, there are several lines  of showstat(asymt) that i am struggling to comprehend, in particular the part which uses the binary selection operator in the following lines :

 try
  r := asympt:-truncate(`limit/eval`(eval(f,x = 1/`limit/X`),n-1,k))
         catch :
  r := undefined
         end try;

@Preben Alsholm thanks i always forget nops

@John Fredsted 

The help page quoted:

Specifically, asympt is defined in terms of the series function:
          subs(x = 1/x, series(subs(x = 1/x, f), x = 0, n))

so an asymptomatic series expansion of a function can be thought of as an ordinary series expansion, however prior to performing it, substituting the arguement 'x' for its reciprocal arguement 1/x, THEN computing the series expansion THEN again performing a substitution of the resulting series's argument with it's reciprocal. im going to check something first, because i have a suspicion that it isnt working as a result of the pole elected,(being x=0) and the zeta of course having a singularity at x=1 so it may work for that.

i posted this question because im getting to the stage where i cant bear any "hidden" procedures being performed by the CAS, i like to know exactly what im computing, and i call asyptm quite frequently in my silly adventures. 

ok thanks that was also my impression

@Christopher2222 i didnt say i suspect he is i was implying he should be.

ok fine maybe that was an exageration but seriously can reputation points be cashed in for bitcoin? if the experts i need to answer my questions on here are not getting paid to do so, then i may as well go back to the maple help interface on the road to becoming such an expert myself. which would then mean im not getting paid to be such an expert either, hence the infinite cycle continues and the space aliens are laughing at our ignorance in aspiring to greatness.

although i admit not having used this site as much as others, the majority of the assistance i have got from here was from the OP of this post, and if his reputation points are any indicator, he has done so for many others.

this then begs the question, if carl isnt on maple's payroll, then who the f@#$ is? space aliens?

@Carl Love yea silly hats are great

@ecterrab yes the ode advisor and function advisor have correspondingly "case scenario"  precise error verbose/ (whatever the word for tell user about it in console is)  output  and this is in stark contrast to whats dispatched in other engines correction other packages.

@tomleslie  also in says toys from pram im assuming you meant justice from COT