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nLab > Latest Changes: cotangent function

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  1.  
    • CommentRowNumber1.
    • CommentAuthorTodd_Trimble
    • CommentTimeMay 10th 2019

    Stub following the same pattern as tangent function.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeMay 10th 2019

    Added remarks on the series expansion of the cotangent.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 11th 2019

    That’s a cool series expansion, and I’m tempted to write it as

    cot(πx)=∑ n∈ℤ1x−n \cot(\pi x) = \sum_{n\in \mathbb{Z}} \frac{1}{x-n}
    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 11th 2019

    Added missing factor of π\pi in infinite sum expression.

    diff, v4, current

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeMay 11th 2019

    Yes, and people often do suggestively write the sum like that, although the convergence is less apparent when written that way.

    Thanks for spotting that missing π\pi on the left.

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 11th 2019
    • (edited May 12th 2019)

    It was John B who pointed it out when I tweeted the cute but incorrect version earlier :-)

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 7th 2023

    Added, among other things, the relation to Bernoulli numbers.

    diff, v8, current

1 to 7 of 7

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