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Math Help - notation.

  1. #1
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    notation.

    if i have:

    for even n,
    An= 4[(-1)^(n/2)-1]/(π^2n^2)

    and for odd n,
    An= 2[πn(-1)^((n-1)/2)-2]/(π^2n^2)

    can i use proper notation to write this all in one line?
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  2. #2
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    Quote Originally Posted by linalg123 View Post
    if i have:

    for even n,
    An= 4[(-1)^(n/2)-1]/(π^2n^2)

    and for odd n,
    An= 2[πn(-1)^((n-1)/2)-2]/(π^2n^2)

    can i use proper notation to write this all in one line?
    Dear linalg123,

    This is a piecewise function. So you could write,

    A_n=\left\{\begin{array}{cc}\dfrac{4\left((-1)^{\frac{n}{2}}-1\right)}{\pi^{2n^2}}&\mbox{ if n is even}\\\dfrac{2\left(\pi n(-1)^{\frac{n-1}{2}}-2\right)}{\pi^{2n^2}} & \mbox{ if n is odd}\end{array}\right.
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  3. #3
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    If A_n is equal to A for n odd and B for n even you can also write it as

    A\frac{1- (-1)^n}{2}+ B\frac{1+ (-1)^n}{2}

    Do you see why?
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