- #1

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is there an alternative way of displaying

##\frac{x}{e^{x}-1}##

as a trigonometric function,

__not__using the bernoulli-numbers ?

Thanks in advance

- Thread starter eaglechief
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- #1

- 26

- 1

is there an alternative way of displaying

##\frac{x}{e^{x}-1}##

as a trigonometric function,

Thanks in advance

- #2

HallsofIvy

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- #3

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Regardless of what it means, writing it this way would not help since it is not true. It is ##e^x##, not ##e^{ix}## ...

- #4

mfb

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Well, you can replace x by ix.

- #5

Svein

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- #6

WWGD

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- #7

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Basically, i am trying to understand, what the Bernoulli Numbers "do" and why they can be developed in a series expansion leading to the simple result x/(e^x-1).

I started by checking that Faulhaber-formulas, where the bernoulli-numbers appear in the last term while summarising x^2n with escalating x. Second, i wonder why they "appear" only with 2n index (except B#1).

thx for any hint !

- #8

Svein

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This may possibly help: https://en.wikipedia.org/wiki/Riemann_zeta_function.Second, i wonder why they "appear" only with 2n index (except B#1).

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