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  • bug in asympt?

    From jfh@21:1/5 to jfh on Mon Nov 16 12:59:14 2020
    On Tuesday, November 17, 2020 at 9:47:49 AM UTC+13, jfh wrote:
    This little program using Maple 2017 (X86 64 LINUX) gave the first few terms of each series correctly according to the NIST Handbook of Mathematical Functions (27.4.5) and (27.2.12) but then gave some wrong ones. Is this a Maple bug or my misuse of
    asympt ?

    for n from 7 to 13
    do
    lprint(simplify(asympt(1/Zeta(s),s,n)));
    od;

    Apology: the output at n=8 was not what I inadvertently posted a few minutes ago but this:

    1-2^(-s)-3^(-s)-5^(-s)+6^(-s)-7^(-s)+2*10^(-s)+12^(-s)+O(14^(-s))

    (The coefficient of N^(-s) should be (-1)^nu if N is the product of nu distinct primes, 1 if N=1, and 0 if N has a repeated prime factor.)

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  • From jfh@21:1/5 to All on Mon Nov 16 12:47:48 2020
    This little program using Maple 2017 (X86 64 LINUX) gave the first few terms of the series correctly according to the NIST Handbook of Mathematical Functions (27.4.5) and (27.2.12) but then gave some wrong ones. Is this a Maple bug or my misuse of asympt
    ?

    for n from 7 to 13
    do
    lprint(simplify(asympt(1/Zeta(s),s,n)));
    od;

    For example the output at n=8 was

    (-s) (-s) (-s) (-s) (-s) (-s) (-s) (-s)
    1 - 2 - 3 - 5 + 6 - 7 + 2 10 + 12 + O(14 )

    n=7 was OK to -7^(-s) but ended with O(10^(-s)),
    n=8 OK to -7^(-s) but ended with O(14^(-s)),
    n=9 OK to +10^(-s) but ended with O(15^(-s)),
    n=10 OK to -11^(-s) but ended with O(15^(-s)),
    n=11 OK to -11^(-s) but ended with O(18^(-s)),
    n=12 OK to -13^(-s) but ended with O(18^(-s)),
    n=13 OK to +14^(-s) but ended with O(20^(-s)),

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