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Nov 16, 2020, 3:47:49 PM11/16/20

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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)),

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)),

Nov 16, 2020, 3:59:15 PM11/16/20

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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 ?

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.)

> 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:
> for n from 7 to 13

> do

> lprint(simplify(asympt(1/Zeta(s),s,n)));

> od;

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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