|
|
A112190
|
|
McKay-Thompson series of class 48e for the Monster group.
|
|
1
|
|
|
1, -1, -1, -1, 0, -1, 0, -1, 1, 0, -2, -1, 1, -1, -1, -2, 2, -2, -2, -1, 1, -2, -2, -2, 4, -3, -4, -4, 2, -4, -2, -4, 5, -4, -6, -5, 5, -6, -5, -7, 8, -7, -8, -7, 6, -8, -8, -9, 13, -12, -14, -13, 10, -14, -10, -14, 17, -14, -20, -17, 17, -19, -18, -22, 24, -24, -26, -24, 22, -26, -26, -29, 37, -34, -39, -38, 32, -40, -34, -42, 48, -44
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,11
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
T48e = 1/q - q - q^3 - q^5 - q^9 - q^13 + q^15 - 2*q^19 - q^21 + q^23 + ...
|
|
MATHEMATICA
|
eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; A:= q*(eta[q^8]*eta[q^12] /(eta[q^4]*eta[q^24]))^3; T24d := A - q^2/A; a:= CoefficientList[ Series[(T24d - 2*q + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 01 2018 *)
|
|
PROG
|
(PARI) q='q+O('q^50); A = (eta(q^8)*eta(q^12)/(eta(q^4)*eta(q^24)))^3; T24d = A - q^2/A; Vec(sqrt(T24d - 2*q)) \\ G. C. Greubel, Jul 01 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|