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Log expansions

  1. Jul 12, 2005 #1
    How Do I Find The Logarithmic Expansions Of Log[x],i Mean The Series Of Log[x].it Is Urgent
     
  2. jcsd
  3. Jul 12, 2005 #2

    Zurtex

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  4. Jul 12, 2005 #3
    The series expansion of any function can be obtained by Taylor's series expansion:
    f(x)=f(a)+(x-a)f'(a)+(x-a)^2f"(a)/2!+(x-a)^3f"'(a)/3!+...

    Using the above formula, any function can be expanded in terms of powers of (x-a), provided that all derivatives of f(x) are defined at x=a.

    Note: logx can not be expanded in terms of powers of x, because the derivatives of logx are not defined at x=0.
     
  5. Jul 12, 2005 #4

    EnumaElish

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  6. Jul 12, 2005 #5

    lurflurf

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    I think you mean log x cannot be expanded about zero in a series of nonnegative powers.
     
  7. Jul 12, 2005 #6
    example can be done via the log(1+x) series |x|<1

    x-x^2/2+x^3/3....
     
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