Strange Series BUg

*To*: mathgroup at yoda.physics.unc.edu (Mathematica User's Group)*Subject*: Strange Series BUg*From*: Keith Clay <clay at galileo.phys.washington.edu>*Date*: Thu, 23 Sep 93 15:06:17 MDT

Here is a bug that calls into question not only the way in which Mma deals with series, but the way in which Mma deals with constants whether they are constants I invent like "z" or one that it is supposed to know about like "Pi". Here is is: ------------------------------------------------------------------------ DEFINE A SIMPLE FUNCTION AND ASK FOR THE SERIES. KEEP YOUR EYES ON "d". In[1]:= expr1 = E^( (a - b x) (c - d) ) (c - d) (a - b x) Out[1]= E In[2]:= Series[expr1,{x,0,1}] a (c - d) a (c - d) 2 Out[2]= E - b (c - d) E x + O[x] NO PROBLEM. IT SHOULDN'T MATTER IF WE LET d BE SOMETHING LIKE Log[z], RIGHT? In[3]:= expr2 = expr1/.(d->Log[z]) (a - b x) (c - Log[z]) Out[3]= E In[4]:= Series[expr2,{x,0,1}] Series::esss: Essential singularity encountered in 2 Exp[a (c - Log[z]) - b (c + <<1>>) x + O[x] ]. (a - b x) (c - Log[z]) Out[4]= Series[E , {x, 0, 1}] SOMEHOW THE PRESENCE OF "z" BOTHERED IT. NOW WE MAKE IT EASIER BY PUTTING A NUMBER LIKE "E" IN THE LOG TERM In[5]:= expr3 = expr2/.z->E (-1 + c) (a - b x) Out[5]= E In[6]:= Series[expr3,{x,0,1}] a (-1 + c) a (-1 + c) 2 Out[6]= E - b (-1 + c) E x + O[x] IT IS EASY TO THINK ABOUT THE LOG OF "E" OR A REAL NUMBER. NO PROBLEM, RIGHT? In[7]:= expr4 = expr2/.z->1.1 (-0.0953102 + c) (a - b x) Out[7]= E In[8]:= Series[expr4,{x,0,1}] a (-0.0953102 + c) a (-0.0953102 + c) 2 Out[8]= E - b (-0.0953102 + c) E x + O[x] FOR SOME REASON HAVING A VARIABLE IN THE LOG FUNCTION THREW MMA OFF, BUT AS LONG AS IT IS JUST A NUMBER, THERE IS NO PROBLEM RIGHT? WRONG!!! In[9]:= expr5 = expr2/.z->Pi (a - b x) (c - Log[Pi]) Out[9]= E In[10]:= Series[expr5,{x,0,1}] Series::esss: Essential singularity encountered in 2 Exp[a (c - Log[Pi]) - b (c + <<1>>) x + O[x] ]. (a - b x) (c - Log[Pi]) Out[10]= Series[E , {x, 0, 1}] This is scary. ------------------------------------------------------------------------ Keith Clay Department of Physics, FM-15 (clay at galileo.phys.washington.edu) University of Washington ( -or- clay at phys.washington.edu ) Seattle, WA 98195