How to find explicit solution for recursive sequences with nonlinear terms?
Are there any general known methodologies or algorithms to derive an explicit equation for a nonlinear sequence? As an example, I am struggling to find an explicit expression for the sequence below:
$a_n=frac{sqrt{a_{n-1}^3+c_0}-c_1}{a_{n-1}-c_2}-a_{n-1}-c_3$
Considering $c_i$ as integer constant parameters, Is it possible to write this as an explicit expression like $a_n=f(a_0, n)$?
My ultimate intention, however, is to find a way so that I could calculate $n$ for any given two consecutive values in the sequence let's say $a_n$ and $a_{n-1}$. Is such thing possible with known math methodologies?
sequences-and-series nonlinear-analysis
asked Jan 6 at 11:22
PouJaPouJa
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Are there any general known methodologies or algorithms to derive an explicit equation for a nonlinear sequence? As an example, I am struggling to find an explicit expression for the sequence below:
$a_n=frac{sqrt{a_{n-1}^3+c_0}-c_1}{a_{n-1}-c_2}-a_{n-1}-c_3$
Considering $c_i$ as integer constant parameters, Is it possible to write this as an explicit expression like $a_n=f(a_0, n)$?
My ultimate intention, however, is to find a way so that I could calculate $n$ for any given two consecutive values in the sequence let's say $a_n$ and $a_{n-1}$. Is such thing possible with known math methodologies?
sequences-and-series nonlinear-analysis
asked Jan 6 at 11:22
PouJaPouJa
134
New contributor
PouJa is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
Are there any general known methodologies or algorithms to derive an explicit equation for a nonlinear sequence? As an example, I am struggling to find an explicit expression for the sequence below:
$a_n=frac{sqrt{a_{n-1}^3+c_0}-c_1}{a_{n-1}-c_2}-a_{n-1}-c_3$
Considering $c_i$ as integer constant parameters, Is it possible to write this as an explicit expression like $a_n=f(a_0, n)$?
My ultimate intention, however, is to find a way so that I could calculate $n$ for any given two consecutive values in the sequence let's say $a_n$ and $a_{n-1}$. Is such thing possible with known math methodologies?
sequences-and-series nonlinear-analysis
asked Jan 6 at 11:22
PouJaPouJa
134
New contributor
PouJa is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Are there any general known methodologies or algorithms to derive an explicit equation for a nonlinear sequence? As an example, I am struggling to find an explicit expression for the sequence below:
$a_n=frac{sqrt{a_{n-1}^3+c_0}-c_1}{a_{n-1}-c_2}-a_{n-1}-c_3$
Considering $c_i$ as integer constant parameters, Is it possible to write this as an explicit expression like $a_n=f(a_0, n)$?
My ultimate intention, however, is to find a way so that I could calculate $n$ for any given two consecutive values in the sequence let's say $a_n$ and $a_{n-1}$. Is such thing possible with known math methodologies?
sequences-and-series nonlinear-analysis
sequences-and-series nonlinear-analysis
asked Jan 6 at 11:22
PouJaPouJa
134
New contributor
PouJa is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 6 at 11:22
PouJaPouJa
134
New contributor
PouJa is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 6 at 11:22
PouJaPouJa
134
New contributor
PouJa is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 6 at 11:22
PouJaPouJa
134
asked Jan 6 at 11:22
PouJaPouJa
134
134
New contributor
PouJa is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
PouJa is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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