A246927 Expansion of psi(-q) * phi(q^3)^2 * chi(q^3) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.
1, -1, 0, 4, -5, 0, 4, -8, 0, 2, -4, 0, 12, -4, 0, 16, -13, 0, 0, -12, 0, 8, -4, 0, 20, -5, 0, 4, -16, 0, 8, -24, 0, 8, -8, 0, 10, -4, 0, 32, -20, 0, 8, -12, 0, 0, -8, 0, 28, -9, 0, 24, -20, 0, 4, -32, 0, 8, -4, 0, 32, -12, 0, 16, -29, 0, 16, -12, 0, 16, -8
Offset: 0
Keywords
Examples
G.f. = 1 - q + 4*q^3 - 5*q^4 + 4*q^6 - 8*q^7 + 2*q^9 - 4*q^10 + 12*q^12 + ...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..2500
- Michael Somos, Introduction to Ramanujan theta functions
- Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
Programs
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Magma
A := Basis( ModularForms( Gamma0(36), 3/2), 70); A[1] - A[2] + 4*A[4] - 5*A[5] + 4*A[6];
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Mathematica
a[ n_] := SeriesCoefficient[ QPochhammer[ -q^3, q^6] EllipticTheta[ 2, Pi/4, q^(1/2)] EllipticTheta[ 3, 0, q^3]^2 / (2^(1/2) q^(1/8)), {q, 0, n}]; -
PARI
{a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^4 + A) * eta(x^6 + A)^12 / (eta(x^2 + A) * eta(x^3 + A)^5 * eta(x^12 + A)^5), n))};
Formula
Expansion of eta(q) * eta(q^4) * eta(q^6)^12 / (eta(q^2) * eta(q^3)^5 * eta(q^12)^5) in powers of q.
Euler transform of period 12 sequence [-1, 0, 4, -1, -1, -7, -1, -1, 4, 0, -1, -3, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = 246^(1/2) (t/i)^(3/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A246926.
Comments