[seqfan] Re: Sum, Product, and subscript formula syntax (was Re: Formula in A060294.)

[Bruno Berselli]

>> My preference is for this style:
>> e = sum_{k=0,1,...} 1/k!
>> Also good is
>> e = sum_{k=0,1,...,oo} 1/k!

>I agree with Neil's preferences, although I think that
>e = sum( 1/k!,  k=0..oo )
>or
>e = sum( k=0..oo, 1/k! )
>is (almost) as good
>(but " sum( k=0, oo, 1/k! ) " is a bit worse and
>the still frequently seen "sum( 1/k!, k, 0, oo )"
>should be banned, IMO.)


Yes, I agree with Maximilian and Neil.

And the form  sum( 1/k!,  k>=0 ) ?

Thanks,


Bruno


________________________________
 Da: Maximilian Hasler <maximilian.hasler at gmail.com>
A: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu> 
Inviato: Lunedì 25 Marzo 2013 13:13
Oggetto: [seqfan] Re: Sum, Product, and subscript formula syntax (was Re: Formula in A060294.)
 
On Mon, Mar 25, 2013 at 7:17 AM, Neil Sloane <njasloane at gmail.com> wrote:
> My preference is for this style:
> e = sum_{k=0,1,...} 1/k!
> Also good is
> e = sum_{k=0,1,...,oo} 1/k!

I agree with Neil's preferences, although I think that
e = sum( 1/k!,  k=0..oo )
or
e = sum( k=0..oo, 1/k! )
is (almost) as good
(but " sum( k=0, oo, 1/k! ) " is a bit worse and
the still frequently seen "sum( 1/k!, k, 0, oo )"
should be banned, IMO.)
--- actually, if there is nothing else following, then
e = sum_{k=0..oo} 1/k!
is nicer, IMO, but e.g. in
  e = sum( k=0..oo, 1/k! ) * pi/2
or
  e = sum( k=0..oo, 1/k! ) * product( ... )
etc, the functional notation clarifies the grouping and avoids any ambiguity
(while " (sum_{...} ...) "  would be possible, too, of course, but add
additional "noise" as JA would say).

In the above I used ".." to denote the summation interval.
I know that this is an artifact of several  CAS and not usual
mathematical notation,
and therefore I did not dare to use it on OEIS, but more recently I
noticed that it had become accepted (IIRC it is / was proposed in
several style sheets).
I think I still do not use it in OEIS, at the cost of adding (at
least) three more (fixed width...!) characters,
a..b => a,...,b
to stick to traditional math notation, but if there is sufficient
concensus, I'd agree on the simplified notation, given that
traditional notation does not require the ",...," in, e.g.,
sum_{k=a}^b

Also, I think that, especially if the formula is long and could break the line,
it is maybe not required to write a,a+1,....,b
since there is not any reason to assume that a,...,b would mean
something else than this. Of course in all other cases (e.g.
a,a+2,a+4,...) a step size different from 1 should be made manifest
explicitely, even if it could follow from the context or nearby
explanations.

(In the special case of "p=2,3,..." but also "q=2,3,..." where there
might be doubts on whether the integers >= 2 or the primes are meant ;
usually p=2,3,5... would suggest the latter, but "p=3,5,7..." again be
ambiguous ; in all these cases I think an *additional* comment should
be added.)

Maximilian



> I don't like
> e = sum_{k=0}^{oo} 1/k!,
> (also based on Latex) which is much less intuitive!
>
> Neil
>
>
>
> On Mon, Mar 25, 2013 at 6:12 AM, Robert Munafo <mrob27 at gmail.com> wrote:
>
>> I don't really mind having different formats because I understand both, but
>> I'm curious: Which of these is the more correct format for subscripts, or
>> specifically for sum and product, in an OEIS formula entry:
>>
>> "Human-readable":  e = sum (k = 0 .. infinity) 1/k!
>>
>> or "TeX-like subscript notation":  e = sum_{k=0,1,...} 1/k!
>>
>> I ask because I noticed that http://oeis.org/A060294 includes examples of
>> both forms:
>>
>> 2/Pi = product (n = 2 .. infinity) (p(n) + 2 - (p(n) mod 4))/p(n), where
>> > p(n) is the n-th prime
>>
>>
>> > 2/Pi = sum_{k=0,1,...} ((2*k)!/(k!)^2)^3*((42*k+5)/(2^{12*k+3}))
>>
>>
>>
>> On Sat, Mar 23, 2013 at 8:36 PM, Paul D Hanna <pauldhanna at juno.com> wrote:
>>
>> > Here is the correction to the poorly written formula:
>> > 2/Pi = 1 - 5(1/2)^3 + 9((1*3)/(2*4))^3 - 13((1*3*5)/(2*4*6))^3 ...
>> >  That is,
>> > 2/Pi = Sum_{n>0} (-1)^n * (4*n+1) * Product_{k=1..n} (2*k-1)^3/(2*k)^3.
>> >     Paul
>> >
>>
>> --
>>   Robert Munafo  --  mrob.com
>>   Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 -
>> mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>
>
> --
> Dear Friends, I have now retired from AT&T. New coordinates:
>
> Neil J. A. Sloane, President, OEIS Foundation
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
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