General question about recursive formula
0
$begingroup$
I have been trying to find an explicit formula for a sequence for a while now. I have found a recursive formula for it.
So my question is : is it possible for a sequence to have a recursive formula but no explicit formula? If so could you please provide an example?
Thank you very much for your time and help!
sequences-and-series real-numbers
asked Dec 6 '18 at 20:32
Victor OrtaVictor Orta
598
$endgroup$
add a comment |
0
$begingroup$
I have been trying to find an explicit formula for a sequence for a while now. I have found a recursive formula for it.
So my question is : is it possible for a sequence to have a recursive formula but no explicit formula? If so could you please provide an example?
Thank you very much for your time and help!
sequences-and-series real-numbers
asked Dec 6 '18 at 20:32
Victor OrtaVictor Orta
598
$endgroup$
1
$begingroup$
Actually, it's only very special recurrences that can be solved explicitly, but it's hard to show that "no explicit formula exists." What is the definition of an explicit formula? It might be as well if you would post the specific recurrence you're working with. Maybe someone will know something about it.
$endgroup$
– saulspatz
Dec 6 '18 at 20:38
$begingroup$
It's a sequence to do with the zeta function. I just wanted to ask since i have been working on it for a few months now and no good results so far.
$endgroup$
– Victor Orta
Dec 6 '18 at 20:44
add a comment |
0
0
0
$begingroup$
I have been trying to find an explicit formula for a sequence for a while now. I have found a recursive formula for it.
So my question is : is it possible for a sequence to have a recursive formula but no explicit formula? If so could you please provide an example?
Thank you very much for your time and help!
sequences-and-series real-numbers
asked Dec 6 '18 at 20:32
Victor OrtaVictor Orta
598
$endgroup$
I have been trying to find an explicit formula for a sequence for a while now. I have found a recursive formula for it.
So my question is : is it possible for a sequence to have a recursive formula but no explicit formula? If so could you please provide an example?
Thank you very much for your time and help!
sequences-and-series real-numbers
sequences-and-series real-numbers
asked Dec 6 '18 at 20:32
Victor OrtaVictor Orta
598
asked Dec 6 '18 at 20:32
Victor OrtaVictor Orta
598
asked Dec 6 '18 at 20:32
Victor OrtaVictor Orta
598
asked Dec 6 '18 at 20:32
Victor OrtaVictor Orta
598
asked Dec 6 '18 at 20:32
Victor OrtaVictor Orta
598
598
1
$begingroup$
Actually, it's only very special recurrences that can be solved explicitly, but it's hard to show that "no explicit formula exists." What is the definition of an explicit formula? It might be as well if you would post the specific recurrence you're working with. Maybe someone will know something about it.
$endgroup$
– saulspatz
Dec 6 '18 at 20:38
$begingroup$
It's a sequence to do with the zeta function. I just wanted to ask since i have been working on it for a few months now and no good results so far.
$endgroup$
– Victor Orta
Dec 6 '18 at 20:44
add a comment |
1
$begingroup$
Actually, it's only very special recurrences that can be solved explicitly, but it's hard to show that "no explicit formula exists." What is the definition of an explicit formula? It might be as well if you would post the specific recurrence you're working with. Maybe someone will know something about it.
$endgroup$
– saulspatz
Dec 6 '18 at 20:38
$begingroup$
It's a sequence to do with the zeta function. I just wanted to ask since i have been working on it for a few months now and no good results so far.
$endgroup$
– Victor Orta
Dec 6 '18 at 20:44
1
1
$begingroup$
Actually, it's only very special recurrences that can be solved explicitly, but it's hard to show that "no explicit formula exists." What is the definition of an explicit formula? It might be as well if you would post the specific recurrence you're working with. Maybe someone will know something about it.
$endgroup$
– saulspatz
Dec 6 '18 at 20:38
$begingroup$
Actually, it's only very special recurrences that can be solved explicitly, but it's hard to show that "no explicit formula exists." What is the definition of an explicit formula? It might be as well if you would post the specific recurrence you're working with. Maybe someone will know something about it.
$endgroup$
– saulspatz
Dec 6 '18 at 20:38
$begingroup$
It's a sequence to do with the zeta function. I just wanted to ask since i have been working on it for a few months now and no good results so far.
$endgroup$
– Victor Orta
Dec 6 '18 at 20:44
$begingroup$
It's a sequence to do with the zeta function. I just wanted to ask since i have been working on it for a few months now and no good results so far.
$endgroup$
– Victor Orta
Dec 6 '18 at 20:44
add a comment |
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1
$begingroup$
Actually, it's only very special recurrences that can be solved explicitly, but it's hard to show that "no explicit formula exists." What is the definition of an explicit formula? It might be as well if you would post the specific recurrence you're working with. Maybe someone will know something about it.
$endgroup$
– saulspatz
Dec 6 '18 at 20:38
$begingroup$
It's a sequence to do with the zeta function. I just wanted to ask since i have been working on it for a few months now and no good results so far.
$endgroup$
– Victor Orta
Dec 6 '18 at 20:44