OFFSET
0,6
COMMENTS
REFERENCES
H. Kahl, G. Koehler, Components of Hecke theta series, J. Math. Anal. Appl. 232 (1999), no. 2, 312-331, see page 320. MR1683136 (2000e:11051)
LINKS
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of f(x)^2 / chi(x)^3 = f(x)^5 / phi(x)^3 = f(-x^2)^2 / chi(x) = f(-x^2) * psi(-x) = f(-x^2)^3 / f(x) = phi(x)^2 / chi(x)^5 = psi(-x)^2 * chi(x) in powers of x where phi(), psi(), chi(), f() are Ramanujan theta functions. - Michael Somos, Jan 29 2015
Expansion of q^(-5/24) * eta(q) * eta(q^4) in powers of q.
Euler transform of period 4 sequence [-1, -1, -1, -2, ...].
G.f. Product_{k>0} (1 - x^k) * (1 - x^(4*k)).
EXAMPLE
G.f. = 1 - x - x^2 - x^4 + 2*x^5 + x^6 + x^7 - x^8 + x^10 - x^11 - x^12 - ...
G.f. = q^5 - q^29 - q^53 - q^101 + 2*q^125 + q^149 + q^173 - q^197 + q^245 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x] QPochhammer[ x^4], {x, 0, n}]; (* Michael Somos, Jan 29 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^4 + A), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, May 09 2005
STATUS
approved