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A novice's problem, perhaps: it seems that /. substitution does weird things to the scope.

In[1]:= alpha := -0.6 + 0.05*k /. k -> 1

In[2]:= mu[k_] := Integrate[x^alpha*x^k, {x, 0, 1}]

In[3]:= Table[mu[k], {k, 0, 2}]

Out[3]= {2.5, 0.689655, 0.4}

In[4]:= Table[mu[p], {p, 0, 2}]

Out[4]= {2.22222, 0.689655, 0.408163}

Why does Table iterated over k produce different results from Table iterated over p? And what exactly does Table over kcompute?

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    $\begingroup$ Do not paste In[], Out[] to your question it it makes it easier to copy your code. $\endgroup$ – user9660 Dec 24 '14 at 14:38
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The reason is that in the first table (Table[mu[k], {k, 0, 2}]) the rule substitution (ReplaceAll) does not happen and k in alpha is always take whatever k came from Table.

to check that try:

alpha := -0.6 + 0.05*1

and then

Table[mu[k], {k, 0, 2}]
(*{2.22222, 0.689655, 0.408163}*)

if you want to go for more details, check in your example this:

Table[mu[k], {k, 0, 2}]//Trace

Table[mu[p], {p, 0, 2}]//Trace
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  • $\begingroup$ Thank you for your answer. Trace outputs lots of stuff I don't know how to interpret yet, unfortunately. Also, I have noticed that if I replace := with = in the definition of alpha, the problem goes away. Why is that so? $\endgroup$ – Pastafarianist Dec 26 '14 at 12:05

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