# Question:Sum from k=0 to k=cst of 0^k

## Question:Sum from k=0 to k=cst of 0^k

Hi everyone,

I'm quite sure that this question has already been answered but I couldn't find any satisfactory explanation (my bad).

I'm wondering why the following expression

sum(0^k, k = 0 .. 0);
yields 0 as result while

0^0;
returns 1

and

sum(1, k = 0 .. 0);
also return 1.

I understand that 0^0;

is an indeterminate form so that its evaluation is a matter of convention but Maple's approach seems to be inconsistent as 0^0;

takes different values depending on the context (symbolic summation/direct evaluation). It particularly yields inconsistent results when rewriting hypergeometric functions in equivalent forms (evaluation the same function under the two forms yields two differents results...)

I guess that there is a valid explanation for this and some good practices to have while playing with such forms.

Thanks to anyone that would redirect to a post/document or answer to this post.

Regards,

Georges.

EDIT: images not showing up when posting (preview was fine)

EDIT2: setting  sum(0^k, k = 0 .. 0) := 1; seems to help maple. I don't understand what it is doing (overriding a definition/convention?)

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