[seqfan] Re: Checking the numerical integration for A355594

Richard J. Mathar mathar at mpia-hd.mpg.de
Sat Aug 20 18:46:13 CEST 2022

hp> Date: Fri, 29 Jul 2022 21:04:13 +0200
hp> From: Hugo Pfoertner <yae9911 at gmail.com>
hp> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
hp> Subject: [seqfan] Checking the numerical integration for A355594
hp> ...
hp> In the sequence https://oeis.org/A355954, the correctness of the calculated
hp> constant depends entirely on the function intnum for numerical integration
hp> in PARI being able to calculate an integral with a very high level of
hp> accuracy if the number of digits for the floating-point calculation is set
hp> to 1000 or even higher, for example.
hp>  ...
hp> Of course, it would be much better than these attempts with brute force if
hp> someone could transform the integration similar to the method shown in
hp> (Cserti 2000) for the square lattice https://oeis.org/A355953 in such a way
hp> that a closed representation of the constant would be found.

Associated proposals for recurrences are now in https://vixra.org/abs/2208.0111 .

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