Partial Fraction

  1. Hello,

    Is there any general formula for the partial fraction of the following function:

    [tex]\frac{1}{(ax_1+1)(ax_2+1)\cdots (ax_L+1)}[/tex]

    I can work for L=3, but it get involved for larger L!!

    Thanks in advance
     
  2. jcsd
  3. Ok... from what ive understood, you want write

    [tex]\frac{1}{(ax_1+1)(ax_2+1)\cdots(ax_L+1)}[/tex]

    as

    [tex]\frac{c_1}{ax_1+1}+\frac{c_2}{ax_2+1}+\cdots+\frac{c_L}{ax_L+1}[/tex]

    where the c's are constants. My question is, what is the variable the c's must be independent of? a or x?
     
  4. a is a constant, and x's are the variables.
     
  5. mathman

    mathman 6,511
    Science Advisor
    Gold Member

    Problems involving partial fractions usually have one variable and many constants. From the appearance of your expression, I assume a is the variable and the x's are constants. In that case the c's will be determined by the x's.
     
  6. yes, right. a is the variable and x's are the constants. I got the general solution expression.

    Thanks
     
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