Methods for assigning values to infinite constructs (ex. sums, products)
$begingroup$
(This question is more to get an overhead view of the topic rather than a well defined answer)
How can one assign values to infinite constructs AND justify them.
What do i mean with infinite constructs, well things like infinite sums or products as well as things like $sqrt{10+sqrt{10+sqrt{10+cdots}}}$ and functions like the R Riemann zeta function.
For sums there is a lot of ways I know of such as the limit of partial sums, Cesàro summation, etc.
but in general if you have something like
$z = f_1(a_1,f_2(a_2,f_3(cdots$
how would you justify that z is the 'correct' value.
(for example when are arguments like due to analitical continuation, convergence appropriate)
sequences-and-series infinite-product
asked Jan 10 at 15:13
Sam CoutteauSam Coutteau
1559
$endgroup$
add a comment |
$begingroup$
(This question is more to get an overhead view of the topic rather than a well defined answer)
How can one assign values to infinite constructs AND justify them.
What do i mean with infinite constructs, well things like infinite sums or products as well as things like $sqrt{10+sqrt{10+sqrt{10+cdots}}}$ and functions like the R Riemann zeta function.
For sums there is a lot of ways I know of such as the limit of partial sums, Cesàro summation, etc.
but in general if you have something like
$z = f_1(a_1,f_2(a_2,f_3(cdots$
how would you justify that z is the 'correct' value.
(for example when are arguments like due to analitical continuation, convergence appropriate)
sequences-and-series infinite-product
asked Jan 10 at 15:13
Sam CoutteauSam Coutteau
1559
$endgroup$
add a comment |
$begingroup$
(This question is more to get an overhead view of the topic rather than a well defined answer)
How can one assign values to infinite constructs AND justify them.
What do i mean with infinite constructs, well things like infinite sums or products as well as things like $sqrt{10+sqrt{10+sqrt{10+cdots}}}$ and functions like the R Riemann zeta function.
For sums there is a lot of ways I know of such as the limit of partial sums, Cesàro summation, etc.
but in general if you have something like
$z = f_1(a_1,f_2(a_2,f_3(cdots$
how would you justify that z is the 'correct' value.
(for example when are arguments like due to analitical continuation, convergence appropriate)
sequences-and-series infinite-product
asked Jan 10 at 15:13
Sam CoutteauSam Coutteau
1559
$endgroup$
(This question is more to get an overhead view of the topic rather than a well defined answer)
How can one assign values to infinite constructs AND justify them.
What do i mean with infinite constructs, well things like infinite sums or products as well as things like $sqrt{10+sqrt{10+sqrt{10+cdots}}}$ and functions like the R Riemann zeta function.
For sums there is a lot of ways I know of such as the limit of partial sums, Cesàro summation, etc.
but in general if you have something like
$z = f_1(a_1,f_2(a_2,f_3(cdots$
how would you justify that z is the 'correct' value.
(for example when are arguments like due to analitical continuation, convergence appropriate)
sequences-and-series infinite-product
sequences-and-series infinite-product
asked Jan 10 at 15:13
Sam CoutteauSam Coutteau
1559
asked Jan 10 at 15:13
Sam CoutteauSam Coutteau
1559
asked Jan 10 at 15:13
Sam CoutteauSam Coutteau
1559
asked Jan 10 at 15:13
Sam CoutteauSam Coutteau
1559
asked Jan 10 at 15:13
Sam CoutteauSam Coutteau
1559
1559
add a comment |
add a comment |
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