|
|
A343445
|
|
Coefficients of the series S(p, q) for which (-sqrt(p))*S converges to the largest real root of x^3 - p*x + q for 0 < p and 0 < q < 2*(p/3)^(3/2).
|
|
1
|
|
|
-1, 1, 3, 24, 315, 5760, 135135, 3870720, 130945815, 5109350400, 225881530875, 11158821273600, 609202488769875, 36422392637030400, 2366751668870964375, 166086110424858624000, 12517749576658530579375
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Based on formulas for series solutions of trinomials given in Eagle article.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2^(n - 1) * Gamma((3*n - 1)/2) / Gamma((n + 1)/2).
a(n) = 2^(n - 1) * ((n + 1)/2)_(n - 1), where (x)_k is the Pochhammer symbol for Gamma(x + k) / Gamma(k).
E.g.f.: (sqrt(3)*sin(arcsin(3*sqrt(3)*x)/3) - 3*cos(arcsin(3*sqrt(3)*x)/3))/3. - Stefano Spezia, May 23 2021
|
|
MATHEMATICA
|
Clear[a]; a = Table[2^(n - 1)Gamma[(3*n - 1)/2]/Gamma[(n + 1)/2], {n, 0, 20}] (* or equivalently *)
Clear[a]; a = Table[2^(n - 1)Pochhammer[(n + 1)/2, n - 1], {n, 0, 20}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|