Proof that this product is transcendental (or not) [closed]
The following products can be expressed using the q-Pochhammer symbol:
$Pi^{infty}_{n=0}left(1+e^{-n}right)=left(-1; frac{1}{e}right)_infty$
$Pi^{infty}_{n=1}left(1-e^{-n}right)=left(frac{1}{e}; frac{1}{e}right)_infty$
Must these two constants be transcendental? I believe they should, but I'm looking for how to prove if they are indeed or are not.
infinite-product
asked Jan 4 at 21:28
El EctricEl Ectric
1549
closed as off-topic by Math1000, jgon, Cesareo, KReiser, Holo Jan 5 at 1:49
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Math1000, jgon, Cesareo, KReiser, Holo
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
The following products can be expressed using the q-Pochhammer symbol:
$Pi^{infty}_{n=0}left(1+e^{-n}right)=left(-1; frac{1}{e}right)_infty$
$Pi^{infty}_{n=1}left(1-e^{-n}right)=left(frac{1}{e}; frac{1}{e}right)_infty$
Must these two constants be transcendental? I believe they should, but I'm looking for how to prove if they are indeed or are not.
infinite-product
asked Jan 4 at 21:28
El EctricEl Ectric
1549
closed as off-topic by Math1000, jgon, Cesareo, KReiser, Holo Jan 5 at 1:49
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Math1000, jgon, Cesareo, KReiser, Holo
If this question can be reworded to fit the rules in the help center, please edit the question.
Your thoughts? $,$
– Math1000
Jan 4 at 22:49
add a comment |
The following products can be expressed using the q-Pochhammer symbol:
$Pi^{infty}_{n=0}left(1+e^{-n}right)=left(-1; frac{1}{e}right)_infty$
$Pi^{infty}_{n=1}left(1-e^{-n}right)=left(frac{1}{e}; frac{1}{e}right)_infty$
Must these two constants be transcendental? I believe they should, but I'm looking for how to prove if they are indeed or are not.
infinite-product
asked Jan 4 at 21:28
El EctricEl Ectric
1549
The following products can be expressed using the q-Pochhammer symbol:
$Pi^{infty}_{n=0}left(1+e^{-n}right)=left(-1; frac{1}{e}right)_infty$
$Pi^{infty}_{n=1}left(1-e^{-n}right)=left(frac{1}{e}; frac{1}{e}right)_infty$
Must these two constants be transcendental? I believe they should, but I'm looking for how to prove if they are indeed or are not.
infinite-product
infinite-product
asked Jan 4 at 21:28
El EctricEl Ectric
1549
asked Jan 4 at 21:28
El EctricEl Ectric
1549
edited Jan 5 at 1:41
El Ectric
asked Jan 4 at 21:28
El EctricEl Ectric
1549
asked Jan 4 at 21:28
El EctricEl Ectric
1549
asked Jan 4 at 21:28
El EctricEl Ectric
1549
1549
closed as off-topic by Math1000, jgon, Cesareo, KReiser, Holo Jan 5 at 1:49
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Math1000, jgon, Cesareo, KReiser, Holo
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Math1000, jgon, Cesareo, KReiser, Holo Jan 5 at 1:49
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Math1000, jgon, Cesareo, KReiser, Holo
If this question can be reworded to fit the rules in the help center, please edit the question.
Your thoughts? $,$
– Math1000
Jan 4 at 22:49
add a comment |
Your thoughts? $,$
– Math1000
Jan 4 at 22:49
Your thoughts? $,$
– Math1000
Jan 4 at 22:49
Your thoughts? $,$
– Math1000
Jan 4 at 22:49
add a comment |
0
active
oldest
votes
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Your thoughts? $,$
– Math1000
Jan 4 at 22:49