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Math Help - Looking for Power Series

  1. #1
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    Looking for Power Series

    Hey there, I know that

    \frac{t}{e^t-1} = \sum_{k=0}^\infty \frac{B_k}{k!} t^k, where B_k are the Bernoulli numbers. I am looking for a sequence a_k, such that \frac{t}{e^t+e^{-t}} = \sum_{k=0}^\infty a_k t^k.

    Any ideas?
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  2. #2
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    Quote Originally Posted by EinStone View Post
    Hey there, I know that

    \frac{t}{e^t-1} = \sum_{k=0}^\infty \frac{B_k}{k!} t^k, where B_k are the Bernoulli numbers. I am looking for a sequence a_k, such that \frac{t}{e^t+e^{-t}} = \sum_{k=0}^\infty a_k t^k.

    Any ideas?
    What about \frac{t}{e^t+e^{-t}}=\frac{e^tt}{e^{2t}+1} =e^t\,\frac{t}{e^{2t}+1} and then you can multiply both series...?

    Tonio
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  3. #3
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    CAn you enlarge on that?
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