[VA] SRC#001 - Spiky Integral

[Valentin Albillo]

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Hi, all:

Thanks for your interest in my SRC#001, some excellent contributions so far, much appreciated. Next Sunday night (GMT+1) I'll post my HP-41C and HP-71B solutions plus extras, but meanwhile I'll comment on some of your recent posts, read on:

pier4r Wrote:Thanks for the post. What does SRC means in this case? Source problem?

Nope, SRC = Semi-Regular Column.

Gerson W. Barbosa Wrote:Here is my conjecture for the exact result when N = 39: 756388295 / 68719476736*Pi

Fully correct. You might want to check the exact result for N=71, namely:

      I(71) = 335205518724079925 / 73786976294838206464 * Pi

which I got by actually computing the integral, then identifying the resulting constant, using dedicated programs I wrote myself (no OEIS involved). It's the hard way but hey, it's fun !

Pjwum Wrote:we can go beyond 10 [...] suggesting that I(N) will be non-zero if and only if N = 4k+3 and N = 4k+4, for k = 0, 1, 2..

Fully correct as well, we have a winner ! Well done, congratulations. 8-)

Gerson (again) Wrote:Sure we can: [...]

{ 0 0 '1/2*π' '1/4*π' 0 0 '1/8*π' '7/64*π' 0 0 '35/512*π' '31/512*π' 0 0 '361/8192*π' '657/16384*π' 0 0 '2055/65536*π' '1909/65536*π' 0 0 '24955/1048576*π' '46923/2097152*π' 0 0 '316301/16777216*π' '299973/16777216*π' 0 0 '4136805/268435456*π' '15796439/1073741824*π' 0 0 '13853361/1073741824*π' '26585247/2147483648*π' 0 0 '756388295/68719476736*π' '182188585/17179869184*π' }

Not the best method, I fear. [...] The evaluation of the integrals would take much, much longer, I guess.

It would take much, much longer or not, depending on how you go about computing them. Your results are correct, congratulations, but without explaining why would you compute the numerators and denominators that way it all seems a "magic trick" unrelated to the problem at hand as the relation to the integral seems shrouded in mystery ... 8-D

Regards.
V.
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