All Questions
Tagged with recursion polynomials
11
questions
4
votes
1
answer
170
views
How can I compute the $n$-th complete Bell polynomial?
I'm interested in computing the n-th complete Bell polynomial
$
B_n(x_1,..., x_n)
$ using the formula given as the last equation in the "Exponential Bell polynomials" section here (I tried ...
- 45
1
vote
2
answers
464
views
Chebyshev polynomials
How could I write the Chebyshev polynomial as a function that uses Nest? Also, how could I write it using recursion?
Furthermore, how can I show that $T_n(x)=\...
- 41
1
vote
1
answer
80
views
Changing initial conditions in a recursive polynomial family definition. Then, finding the generation function for this family
I'm following a paper trying to find a way to repeat the done computations using Mathematica. I'm beginner using Mathematica and I already read that:
I could define functions by recursion;
I could ...
- 165
1
vote
1
answer
97
views
Recurrences with some relation to Dedekind eta functions
Dedekind eta functions are know to satisfy certain difference equations/recurrence relations. The same is true for ratios of eta functions. Suppose some ratio of eta functions, say $A(q)$ satisfies ...
- 365
5
votes
1
answer
171
views
Fishing for monomials in a nested or partially factored polynomial stream
I have a problem where I'd like to be able to take a multivariate polynomial whose variables are nonscalar and is not written explicitly as a sum of it's nonzero monomial terms and determine which ...
- 1,230
2
votes
1
answer
158
views
Recurrence relation for multivariate polynomials
I am trying to define a function which recursively computes a polynomial associated to every binary string:
ComputePoly[s_]:=(** Recurse on the string s**)
For ...
- 693
3
votes
2
answers
796
views
Transform recursion for coefficients into differential equation for generating function
Assume, one is given a linear recursion with polynomial coefficients for a sequence $(a_i)_i$, such as
a[i] == i a[i-1]
I would like to convert this recursion ...
- 1,395
6
votes
3
answers
710
views
Implementation of a complex recurrence relation for polynomials
I would like to implement the recurrence relation for the polynomials $U_n(x)$ that appear in the large-order asymptotics of the modified Bessel functions.
The recurrence in question is
$$U_{n+1}(x)=\...
- 163
1
vote
3
answers
498
views
List of Tribonacci Polynomials with Mathematica? [duplicate]
I want to list top ten of Tribonacci polynomials. I have following algorithm, but it doesnt work.
...
user2444
12
votes
2
answers
707
views
How to deduce a generator formula for a polynomial sequence?
Consider a polynomial sequence $\{p_n\}$ generated by some (simple) rule:
$$
\begin{array}{l}
p_1(x)=x \\
p_2(x)=2 x-x^2 \\
p_3(x)= x^3-3 x^2+3 x \\
p_4(x)=-x^4+4 x^3-6 x^2+4 x \\
p_5(x)= x^5-5 x^4+...
- 12.7k
5
votes
1
answer
2k
views
Polynomial Approximation from Chebyshev coefficients
I would like to expand a function $f(r)$ in the domain $[0,R]$, around the points $r =0$, and $r = R$ in the following manner
$f(r = 0) = \Sigma_{i=0,i = even}^{imax} f_i (r/R)^i$
and
$f(r = R) = ...
- 499