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Math Help - Series Expansion for tan(x)

  1. #1
    Rhymes with Orange Chris L T521's Avatar
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    Series Expansion for tan(x)

    Is there a generalized form for the Maclaruin Series for tan(x)?

    I started computing the first several terms and it is very tedious...

    I got this far:

    \tan(x)=x+\frac{x^3}{3}+\frac{2x^5}{15}+\frac{17x^  7}{315}+...

    --Chris
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    Is there a generalized form for the Maclaruin Series for tan(x)?

    I started computing the first several terms and it is very tedious...

    I got this far:

    \tan(x)=x+\frac{x^3}{3}+\frac{2x^5}{15}+\frac{17x^  7}{315}+...

    --Chris
    a_n=\frac{(-1)^n2^{2n+2}(2^{2n+2}-1)B_{2n+2}x^{2n+1}}{(2n+2)!}

    Where B_n denotes the nth Bernoulli number
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