Talk:Clausen function
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The current formula seems inconsistent with the structural coherence of the Sl-type recurrence. Direct computation (for example, the case m=0) shows the discrepancy. The corrected form involves Sl, not Cl, in accordance with the integral representation. — Preceding unsigned comment added by IgnorabimusX (talk • contribs) 04:18, 9 September 2025 (UTC)
Log cosine
[edit]@Matthiaspaul: where is Log cosine function defined here? fgnievinski (talk) 04:54, 5 December 2024 (UTC)
Formulas in "Relation to Bernoulli polynomials"
[edit]Hi, the formulas in the mentioned section are not referenced anywhere, and upon close inspection, they seem wrong.
The formulas given for the SL-type Clausen functions imply that, when the index is even, the function is even in theta, and when the index is odd, they are odd in theta, because their Fourier expansions have only cosines and sines, respectively.
However, the formulas relate them to Bernoulli polynomials, which are never even or odd functions in theta. One can see this for the first few explicit evaluations. If they were even or odd, they would only have even or odd powers of theta, respectively. But they don't... Lambdarice (talk) 17:04, 17 May 2025 (UTC)
Integrals of the direct function (SL-type)
[edit]The current formula seems inconsistent with the structural coherence of the Sl-type recurrence. Direct computation (for example, the case m=0) shows the discrepancy. The corrected form involves Sl, not Cl, in accordance with the integral representation. IgnorabimusX (talk) 04:21, 9 September 2025 (UTC)