# FunctionPoles with arbitrary undefined function

Good day everyone. I have very simple question about behaviour of the functions FunctionPoles, FunctionMeromorphic e.t.c. Can these functions work properly with undefined functions? For example when I wrote:

FunctionPoles[1/(k^2 + Subscript[\[Omega], 1]), Subscript[\[Omega], 1]]


I obtained

{{-k^2, 1}}


But If I try to insert an undefined function $$B(k)$$ like that:

FunctionPoles[1/(k^2 + B[k] + Subscript[\[Omega],
1]), Subscript[\[Omega], 1]]


Then I did not obtain expected result. I also tried use Assumptions option but alas have no success. Is there a way to make it work properly? Thanks in advance!

• What do you expect as the output? Apr 1, 2023 at 17:20
• {{-k^2-B[k], 1}} Apr 1, 2023 at 17:23
• If you write FunctionPoles[1/(B + k^2 + ω1), ω1], it returns {{-B-k^2,1}}. Apr 1, 2023 at 17:40
• Alas I need it to be of form B[k] because I have a lot of such expressions with B[k],B[q] and B[k-q] Apr 1, 2023 at 18:44

FunctionPoles[1/(k^2 + B + Subscript[\[Omega],1]), Subscript[\[Omega], 1]]/.B->B[k]

{{-k^2 - B[k], 1}}
BTW, FunctionSingularities[1/(k^2 + B[k] + Subscript[\[Omega], 1]), Subscript[\[Omega], 1]] works well.