reviewed

approved

proposed

reviewed

Peter Bala: The formula is arctanh(1/z) = Sum_{n >= 1} 1/(n*P(n, z)*P(n-1,z)) valid for for complex z not in the closed interval [-1, 1]. I expect this is known but a quick Google search didn't turn up anything so I wrote up a proof and uploaded  a pdf file to A003881.

Peter Bala: I also have some other series for arctan(x) in an old (badly written and disorganised) document uploaded to A002162 (see page 8).

editing

proposed

Joerg Arndt: Wow, do you have an expression like that for (say) arctan(1/x) ?  (I am a bit of a fan of arctan formulas)

arctan(1/239) = Sum_{n >= 1} i/(n*P(n, 239*i)*P(n-1, 239*i)) = 1/239 - 1/40955996 + 1/8773020079176 - 1/1948832181801673304 + 4/1753293766205137615850855 - ...., - ..., where i = sqrt(-1) and P(n, x) denotes the n-th Legendre polynomial. - Peter Bala, Mar 21 2024

arctan(1/239) = Sum_{n >= 1} i/(n*P(n, 239*i)*P(n-1, 239*i)) = 1/239 - 1/40955996 + 1/8773020079176 - 1/1948832181801673304 + 4/1753293766205137615850855 - ...., where i = sqrt(-1) and P(n, x) denotes the n-th Legendre polynomial. - Peter Bala, Mar 21 2024

approved

editing

proposed

approved

editing

proposed

Michel Marcus: I don't agree with the change you did : for me it was the wrong move to do

Michel Marcus: And it was done without notice

Michel Marcus: And now after this fait accompli, you propose a debate ...

Frank Ellermann: The "history" (one day, March 13) is visible in https://oeis.org/draft/A014561  The Style Guide was inconsistent, I supported and suggested your From-idea to fix it, that was rejected. Then I suggested a consistent "Comment from", that was accepted. Consistent is good enough for me.

Jon E. Schoenfield: I just now saw some of the recent (last few weeks) changes to the Style Sheet, and some of them have me thoroughly confused.  E.g. (by which I mean "for example"):

<< Product_{k=a..b} for product notation (always use capital "P"), e.g., Product_{k->infinity} a(k) >>

How is what follows the "e.g." there an example of what precedes it??

More importantly, what does

     Product_{k->infinity} a(k)

mean??  Does it mean

     Product_{k=0..infinity} a(k)
or
     Product_{k=1..infinity} a(k)

or something else?

<<  Sum_{k=a..b} for summation notation (always use capital "S"), e.g., Sum_{n>=1} a(n)  >>

Again, how is what follows the "e.g." an example of what precedes it??

I think there need to be some discussions on a number of recent changes to the Style Sheet.  For now, I think it's best that I put my OEIS editing on hold until these issues are resolved (and instead spend my available time on pandemic response).

Best wishes to all, and stay safe if possible,
-- Jon

Frank Ellermann: @Jon, your fix on A333601 inspired my k->infinity. It's a wiki, just replace it by Product_{k=1..n} from A333601. My edit summaries (visible in the history) were "highlighted Product_{…} and Sum_{…} after a hilarious struggle to grok these notations on OEIS:draft/A333601)" followed by "In this section "k=a..b" is abstract syntax for 'any index, not limited to from..to')", there's no doubt whose fault it was if it was wrong.

Frank Ellermann: @Jon, fixed that per your suggestion, k=1..n, and it took more than 5 minutes, because ">" instead of ">" in the markup confused the Wiki.

proposed

editing

Frank Ellermann: I suggested your idea, that was rejected, I suggested Comment from, that was accepted. If you want to debate that start at https://oeis.org/wiki/Talk:Style_Sheet#Conflicting_style_guidelines_for_a_multi-line_Comment_from

editing

proposed

Michel Marcus: no you changed the stylesheet , but you changed the wrong place

FromComment from Frank Ellermann, Mar 01 2020: (Start)

proposed

editing

Frank Ellermann: https://oeis.org/wiki/Style_Sheet#Comments
https://oeis.org/wiki/Style_Sheet#Signing_your_name_when_you_contribute_to_an_existing_sequence