Expression 4: "r" left parenthesis, "k" , "x" , right parenthesis equals left parenthesis, negative 1 , right parenthesis Superscript, "k" , Baseline "k" ! Start sum from "j" equals 0 to "k" , end sum, StartFraction, "x" Superscript, "k" minus "j" , Baseline Over left parenthesis, "k" minus "j" , right parenthesis ! squared "j" ! , EndFractionrk,x=−1kk!k∑j=0xk−jk−j!2j!
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Expression 5: "p" left parenthesis, "x" , right parenthesis equals Start product from "j" equals 1 to length left parenthesis, "c" Subscript, "s" , Baseline , right parenthesis , end product, "r" left parenthesis, "c" Subscript, "s" , Baseline left bracket, "j" , right bracket , negative "x" , right parenthesis Has graph. To audio trace, press ALT+T.px=lengthcs∏j=1rcsj,−x
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Expression 6: "w" equals Start integral from 0 to infinity , end integral, "e" Superscript, negative "x" , Baseline "p" left parenthesis, "x" , right parenthesis "d" "x" equals 487092w=∫∞0e−xpxdx