I use the below method.
But this method doesn't work for this situation. Why? I have the same results. This is my minimal file and I use texlive 2015. This problem is about \prod too. Thanks for your responsibility.

I want this one in ams style:       
text text text text text text text text text text text text  
and this one in mathabx style:  
But both of them are the same and I don't like it .....

enter image description here

  • 2
    \sum is just a numeric reference to a character in the operators font for the current math settings, so \amssum and \ptmxsum have identical definitions. – David Carlisle Dec 21 '17 at 9:55
  • @David Carlisle Thanks my dear. So how can i use both of them in my file? – SH.Madadpour Dec 21 '17 at 10:03
  • @Steven B. Segletes Thanks a lot my master ...and ...Thanks again. – SH.Madadpour Dec 21 '17 at 10:29

Since it seems you added \prod to the question, I take my answer at Different Sum signs, and using the \fonttable (commented in the MWE), determine the slots for text and display style \prod as 81 and 89, respectively.

% =============================================
%Import symbols from font cmex without importing the whole package
% =============================================
\DeclareFontFamily{U} {cmex}{}

  <-8> cmex7
  <8-9> cmex8
  <9-10> cmex9
  <10-> cmex10}{}

\DeclareSymbolFont{Xcmex} {U} {cmex}{m}{n}

% =============================================
sum and prod under mathptmx:\par
$\sum_{i=1}^2 x_i \ne \prod_{i=1}^2 x_i$
\[\sum_{i=1}^2 x_i \ne \prod_{i=1}^2 x_i \]
Defined Xsum and Xprod from cmex:\par
$\Xsum_{i=1}^2 x_i \ne \Xprod_{i=1}^2 x_i$
\[\Xsum_{i=1}^2 x_i \ne \Xprod_{i=1}^2 x_i\]

enter image description here

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