On Wednesday, September 27, 2017 at 2:39:18 AM UTC+13, Peter Luschny wrote:
restart;
for n from 1 to 10 do product(1 - exp(-3*Pi*k), k=1..n): print(evalf(%,100)) od:
product(1 - exp(-3*Pi*k), k=1..infinity);
0.99991930048242969540076079496607565337604701848050587887793116\
61874620768881558525000761137393119619
0.99991929397054310783846071160943458949489722010393675884188157\
72031677006591102859909094004128441835
0.99991929397001760173579420925756466546613464451769578307221030\
46217577981046063251917225329379286853
0.99991929397001755932770524384215301951312111267396474761039494\
20757198264951861082576558744213889585
0.99991929397001755932428293152156543805216017938155162138450575\
61250456780918293082240670461486937285
0.99991929397001755932428265534261219172472361853070175691267253\
46521158633329104110223861614216303137
0.99991929397001755932428265532032468343467328512694304556439538\
78114792276826418913831611248576903856
0.99991929397001755932428265532032288484350643390064827565514682\
19527120690353372085351014843732960367
0.99991929397001755932428265532032288469836099442954308820325275\
36799279287625628587601960477165670312
0.99991929397001755932428265532032288469834928126260024016748022\
44320939278639343076761038920987656959
0
?
With Maple 2017 (X86 64 LINUX) I got a different result:
product(1 - exp(-3*Pi*k), k=1..infinity);
infinity
--------'
' | |
| | (1 - exp(-3 Pi k))
| |
| |
k = 1
evalf(product(1 - exp(-3*Pi*k), k=1..infinity),100);
0.9999192939700175593242826553203228846983492803172770315323192841366570017\
065263132093348972377771038
but what surprised me was
assume(s<1/2,s>0);
product(1-s^k,k=1..infinity);
product: "Cannot show that 1-s^k has no zeros on [1,infinity]"
infinity
--------'
' | | k
| | (1 - s~ )
| |
| |
k = 1
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