1,597 reputation
32
bio website mobiusfunction.wordpress.com
location
age
visits member for 3 years, 1 month
seen Apr 16 at 14:05

Table[Limit[ Zeta[s]*Sum[(1 - If[Mod[k, n] == 0, n, 0])/k^(s - 1), {k, 1, n}], s -> 1], {n, 1, 12}]

Table[Limit[ Zeta[s] Total[1/Divisors[n]^(s - 1)*MoebiusMu[Divisors[n]]], s -> 1], {n, 1, 32}]

https://oeis.org/A177885

Plot[Im[LogGamma[1/4 + I*t/2]/Pi - I*t/(2*Pi)*Log[Pi] + Log[Zeta[1/2 + I*t]]/Pi + I], {t, 0, 60}, ImageSize -> Large]

Round[Chop[ N[Table[Im[LogGamma[1/4 + I*t/2]]/Pi - t/(2*Pi)*Log[Pi] + Im[Log[Zeta[1/2 + I*t]]]/Pi + 1, {t, 0, 100}]]]]

From this answer: http://math.stackexchange.com/a/442686/8530

This Excel Spreadsheet formula uses Andre LeClaire's formula to approximate the Riemann zeta zeros:

=IF(OR(ROW()=1; COLUMN()=1);0; IF(ROW()>=COLUMN();EXP(-(1-11/8/(COLUMN()-1))/EXP(1)*SUM(INDIRECT(ADDRESS(ROW()-COLUMN()+1; COLUMN(); 4)&":"&ADDRESS(ROW()-1; COLUMN(); 4); 4)));0))

(European dot-comma)

you need to divide the result with: /2/PI()/EXP(1) and take the reciprocal. tetration this is.


This user has not answered any questions
This user has not participated in any tags
This user has not asked any questions
Mathematics 1,597 rep 920
MathOverflow 193 rep 6
Mathematica 180 rep 4
Chemistry 153 rep 4
Stack Overflow 148 rep 4

40 Votes Cast

all time   by type   month  
40 up 26 question 6
0 down 14 answer