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Bug in Sum[] or in funtion definitions?


Hello
The Sum[] seems to ignore special cases of a function. Try the
following:

c[n_] := k cc^n;
c[1] := cc;
Sum[c[m], {m, 1, Infinity, 1}] // FullSimplify
c[1] + Sum[c[m], {m, 2, Infinity, 1}] // FullSimplify
Sum[k cc^n, {n, 1, Infinity, 1}] // FullSimplify
c[1]

Obviously the special case
c[1] := cc
is completely ignored by Sum[].
As I understand this is a bug in the Sum[] or in internal work with
function definitions.
The corresponding pages of the Documentation are:
tutorial/MakingDefinitionsForFunctions
and
tutorial/TheOrderingOfDefinitions


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